Question

How do i solve for x by using natural log (in)?

Answer 1

Unfortunately you cannot use logs to solve this.

However, it shouldn't take too long to use guess-and-check to see that

$2^x+3^x = 2^2+3^2 = 4+9 = 13$

Showing that x = 2 is the solution to the equation.

You can use a graphing calculator to graph out $y = 2^x+3^x$  and  $y = 13$. The two curves cross at (2,13). The x coordinate of that intersection is what we're after. GeoGebra and Desmos are two free options you can pick from in terms of a graphing calculator.