Question

Solve the equation shown below for x. Round your answer to the nearest thousandth: 15=3+3_7 O A. 1.921 O B.-3.678 O C. -1.079 O D. 4.921

Answer 1

To solve for x:

$15=5^{x+3}-7$

On simplification we get,

$\begin{gathered} 15+7=5^{x+3} \\ 22=5^{x+3} \\ 5^{x+3}=22 \end{gathered}$

Taking log base 5 on both sides, we get,

$\begin{gathered} x+3=\log _522 \\ x+3=1.92057 \\ x=1.92057-3 \\ x=-1.07943 \end{gathered}$

Hence, the value of x is -1.079 (Rounded to the nearest thousandth).

Therefore, the correct option is C.