Question

Hi I’m looking to get a step by step solution in solving this problem preparing for my test

Answer 1

To find the solution of the equation we need to remember that the logarithm functions and the exponential functions are inverse of each other that is:

$\log_bb^x=x$

Then we apply the correct logarithm to both sides of the equation to get:

$\begin{gathered} 3^x=17 \\ \log_33^x=\log_317 \\ x=\log_317 \end{gathered}$

Now, if we want to write the solution in terms of the natural logarithm, we need to remember that:

$\log_bx=\frac{\ln x}{\ln b}$

Therefore, the solution of the equation can be express in the two following ways:

$\begin{gathered} x=\log_317 \\ \text{ or} \\ x=\frac{\ln17}{\ln3} \end{gathered}$