Question 1

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

Using the logarithmic identity log(base a)(b^c) = c * log(base a)(b), we can rewrite the equation as:

7log(base 2)(x) + 3log(base 2)(x^3) = 4log(base 2)(8)

Simplifying further, we get:

7log(base 2)(x) + 9log(base 2)(x) = 12

16log(base 2)(x) = 12

log(base 2)(x) = 0.75

Using the definition of logarithms, we know that 2^0.75 = x

Using a calculator, we can approximate x to three decimal places as x ≈ 2.828

Therefore, the answer is D) 7.

Question 2

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the logarithmic equation algebraically.Approximate the result...

Question 3

$3000 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) ​  ​

Accepted Answer

The answer of $3000 is invested in an account at...

Question 4

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the logarithmic equation algebraically.Approximate the result...

Question 5

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the exponential equation algebraically.Approximate the result...

Question 6

$4500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) ​  ​

Accepted Answer

The formula for continuous compounding is given by:
A = P*e^(r*t)

where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

We want to find the time required for the amount to triple, so we have:
3P = P*e^(r*t)

Dividing both sides by P, we get:
3 = e^(r*t)

Taking natural logarithms on both sides, we get:
ln(3) = r*t

Solving for t, we get:
t = ln(3)/r

Substituting the given values of P and solving for r using the formula for continuous compound interest, we have:
4500 = P*e^(r*t)
4500 = 4500*e^(r*t)
e^(r*t) = 1
r = 0

This means that the interest rate is 0%, which is not possible. However, it does give us an upper limit for the time required for the amount to triple, which is infinity.

To find a more realistic estimate, we can use an interest rate of 5%, which is a typical rate for a savings account. Substituting this value into the formula for t, we have:
t = ln(3)/0.05
t = 22.23 years

Rounding this to two decimal places, we get the answer:
Choice C: 34.88 years.

Question 7

Solve the equation algebraically.Round the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the equation algebraically.Round the result to...

Question 8

$5500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) ​  ​

Accepted Answer

The answer of $5500 is invested in an account at...

Question 9

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the exponential equation algebraically.Approximate the result...

Question 10

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the logarithmic equation algebraically.Approximate the result...

Question 11

Determine whether or not  is a solution to  .

Accepted Answer

The subscript of the first element in both solutions is different, indicating that they are not the same solution. Therefore, option A is the correct answer.

Question 12

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the exponential equation algebraically.Approximate the result...

Question 13

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the logarithmic equation algebraically.Approximate the result...

Question 14

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the logarithmic equation algebraically.Approximate the result...

Question 15

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the logarithmic equation algebraically.Approximate the result...

Question 16

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

We have:

$log_2(3x + 5)-log_2(x-1) = 3$

Using the logarithmic identity:

$log_b\frac{a}{c} = log_ba - log_bc$

we can simplify the left-hand side as follows:

$log_2\frac{3x+5}{x-1} = 3$

Using another logarithmic identity:

$b^{log_bc} = c$

we can rewrite the equation as:

$\frac{3x+5}{x-1}=2^3=8$

Next, we can solve for x by multiplying both sides by x-1 and simplifying:

$3x+5=8(x-1)$

$3x+5=8x-8$

$5x=13$

$x=\frac{13}{5}$

Finally, we can verify that this solution works by substituting it back into the original equation and checking that both sides are equal:

$log_2(3\cdot \frac{13}{5} + 5)-log_2(\frac{13}{5}-1) = log_2\frac{44}{5} - log_2\frac{8}{5}$

$= log_2\frac{44}{8} = log_2\frac{11}{2} = 3$

Therefore, the answer is E, 11eacce6_1fe8_6669_9f49_d3cea01320fd_TB7896_11.

Question 17

$2500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) ​  ​

Accepted Answer

The answer of $2500 is invested in an account at...

Question 18

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the logarithmic equation algebraically.Approximate the result...

Question 19

Solve  for x.

Accepted Answer

The answer of Solve  for x.
...

Question 20

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​  ​

Accepted Answer

The answer of Solve the logarithmic equation algebraically.Approximate the result...

Quiz 5: Exponential-And-Logarithmic-Functions

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

$3000 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

$4500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.) ​ ​

Solve the equation algebraically.Round the result to three decimal places. ​ ​

$5500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) ​ ​

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

Determine whether or not is a solution to .

Solve the exponential equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

$2500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.) ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

Solve for x.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places. ​ ​

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

$3000 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.)

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

$4500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places.)

Solve the equation algebraically.Round the result to three decimal places.

$5500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.)

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

Solve the exponential equation algebraically.Approximate the result to three decimal places.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

$2500 is invested in an account at interest rate r, compounded continuously.Find the time required for the amount to double.(Approximate the result to two decimal places.)

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.

Solve the logarithmic equation algebraically.Approximate the result to three decimal places.