Solve the exponential equation. Round your answer to two decimal places. $7 ^ { x + 3 } - 5 = 18$
A) x= -0.77
B) $x = - 1.64$
C) $x = - 1.39$
D) $x = 3.49$
E) $x = - 0.69$

Question

Quizplus · Accepted Answer

To solve for x, we can start by isolating the exponential term:
$$7 ^ { x + 3 } = 23$$
Then, take the logarithm of both sides with base 7:
$$(x+3)\log_7(7)=\log_7(23)$$
Simplifying,
$$x+3=\frac{\log_7(23)}{\log_7(7)}$$
$$x+3=\log_{7}(23)$$
$$x=\log_{7}(23)-3$$
Using a calculator, we get:
$$x\approx -1.39$$
Therefore the answer is C).

Solve the Exponential Equation 7x+3−5=187 ^ { x + 3 } - 5 = 187x+3−5=18

Solve the Exponential Equation $7 ^ { x + 3 } - 5 = 18$