Respuesta :
Let's rewrite the equation:
[tex]5^{x_{}+2}=16[/tex]To answer this question, we can start by applying log in both sides. We can choose the base of the log, let's use base 10, which is the most common one:
[tex]\log (5^{x+2})=\log (16)_{}[/tex]Now we use a the following property of log:
[tex]\log _bx^a=a\cdot\log _bx[/tex]So:
[tex]\begin{gathered} (x+2)\log (5)=\log (16) \\ x+2=\frac{\log (16)_{}}{\log (5)} \\ x=\frac{\log(16)_{}}{\log(5)}-2 \end{gathered}[/tex]We can use a calculator to get the log(16) and log(5). Alternatively, we can use a table of log base 10 values. We get:
[tex]\begin{gathered} x=\frac{1.204119983\ldots}{0.698970004\ldots}-2 \\ x\approx1.72271-2 \\ x\approx-0.27729\approx-0.277 \end{gathered}[/tex]So, the value of x to the nearest thousandths is -0.277.
