Question 1

Use the change-of-base property to find the decimal approximation of the following logarithm. Round the answer to four decimal places, if necessary.

Accepted Answer

The answer of Use the change-of-base property to find the...

Question 2

Find x .

Accepted Answer

The answer of Find x . ...

Question 3

Solve the exponential equation.

Accepted Answer

The answer of Solve the exponential equation. 
...

Question 4

Find x .

Accepted Answer

The answer of Find x . ...

Question 5

Simplify the following expression.

Accepted Answer

The answer of Simplify the following expression. ...

Question 6

Find a decimal approximation of the following natural logarithm. ln 100,000

Accepted Answer

The natural logarithm of 100,000 is approximately 11.5129.

Question 7

Solve the exponential equation.

Accepted Answer

The answer of Solve the exponential equation. 
...

Question 8

Find a decimal approximation of the following natural logarithm. ln 3,350

Accepted Answer

The natural logarithm of 3,350 can be approximated using a calculator or computational tool, and it is closest to 8.1167 among the given options.

Question 9

Solve the exponential equation. Round the answer to four decimal places, if necessary.

Accepted Answer

The answer of Solve the exponential equation. Round the answer...

Question 10

Use the properties of logarithms to expand the following expression.

Accepted Answer

The answer of Use the properties of logarithms to expand...

Question 11

Use the change-of-base property to find the decimal approximation of the following logarithm. Round the answer to four decimal places, if necessary.

Accepted Answer

The answer of Use the change-of-base property to find the...

Question 12

Find a decimal approximation of the following natural logarithm. ln 350

Accepted Answer

ln 350 = 5.8579 (approx)

Question 13

Use the change-of-base property to find the decimal approximation of the following logarithm. Round the answer to four decimal places, if necessary.

Accepted Answer

The answer of Use the change-of-base property to find the...

Question 14

Find a decimal approximation of the following natural logarithm. ln 0.341

Accepted Answer

The answer of Find a decimal approximation of the following...

Question 15

Solve the exponential equation. Round the answer to four decimal places, if necessary.

Accepted Answer

The answer of Solve the exponential equation. Round the answer...

Question 16

Find x .

Accepted Answer

The answer of Find x . ...

Question 17

Solve the exponential equation. Round the answer to four decimal places, if necessary.

Accepted Answer

We can rewrite the exponential equation as:

$3^{x-1} = 10 - 3^x$

Now, we can solve for x numerically using a graphing calculator or computer software. One way to do this is to plot the two functions $y=3^{x-1}$ and $y=10-3^x$ and look for their intersection point(s).

Alternatively, we can use algebraic techniques to rearrange the equation into a more convenient form. For example, we can rewrite it as:

$3^{x-1} + 3^x - 10 = 0$

Let $y = 3^{x-1}$. Then, the equation becomes:

$y + 3y - 10 = 0$

Solving for y, we get:

$y = \frac{10}{4} = 2.5$

Substituting back, we have:

$3^{x-1} = 2.5$

Taking the logarithm of both sides (with any base), we get:

$(x-1) \log 3 = \log 2.5$

Solving for x, we get:

$x = \frac{\log 2.5}{\log 3} + 1 \approx 2.5848$

Rounding to four decimal places, we get:

$x \approx 2.585$

Question 18

Solve the exponential equation. Round the answer to four decimal places, if necessary.

Accepted Answer

The answer of Solve the exponential equation. Round the answer...

Question 19

Use the change-of-base property to find the decimal approximation of the following logarithm. Round the answer to four decimal places, if necessary.

Accepted Answer

The answer of Use the change-of-base property to find the...

Question 20

The annual rate of depreciation r on a car that is purchased for P dollars and is worth W dollars t years later can be found from the formula:  The car depreciates in value according to the following depreciation table. AGE IN YEARS VALUE IN DOLLARS new 4 7,150 5,750 Find the annual rate of depreciation. Round the result to the nearest tenth. __________%

Accepted Answer

The answer of The annual rate of depreciation r on...

Quiz 11: Exponential Functions

Use the change-of-base property to find the decimal approximation of the following logarithm. Round the answer to four decimal places, if necessary.

Find x .

Solve the exponential equation.

Find x .

Simplify the following expression.

Find a decimal approximation of the following natural logarithm. ln 100,000

Solve the exponential equation.

Find a decimal approximation of the following natural logarithm. ln 3,350

Solve the exponential equation. Round the answer to four decimal places, if necessary.

Use the properties of logarithms to expand the following expression.

Use the change-of-base property to find the decimal approximation of the following logarithm. Round the answer to four decimal places, if necessary.

Find a decimal approximation of the following natural logarithm. ln 350

Use the change-of-base property to find the decimal approximation of the following logarithm. Round the answer to four decimal places, if necessary.

Find a decimal approximation of the following natural logarithm. ln 0.341

Solve the exponential equation. Round the answer to four decimal places, if necessary.

Find x .

Solve the exponential equation. Round the answer to four decimal places, if necessary.

Solve the exponential equation. Round the answer to four decimal places, if necessary.

Use the change-of-base property to find the decimal approximation of the following logarithm. Round the answer to four decimal places, if necessary.