Question

5^x+2 = 16 Round to the nearest thousandth.

Answer 1

Let's rewrite the equation:

`5^{x_{}+2}=16`

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:

`\log (5^(x+2))=\log (16)_{}`

Now we use a the following property of log:

`\log _bx^a=a\cdot\log _bx`

So:

`\begin{gathered} (x+2)\log (5)=\log (16) \\ x+2=\frac{\log (16)_{}}{\log (5)} \\ x=\frac{\log(16)_{}}{\log(5)}-2 \end{gathered}`

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:

`\begin{gathered} x=(1.204119983\ldots)/(0.698970004\ldots)-2 \\ x\approx1.72271-2 \\ x\approx-0.27729\approx-0.277 \end{gathered}`

So, the value of x to the nearest thousandths is -0.277.