Find for x to four significant digits. 7^x=13

X ≈ 1.31812322 

X is approximately the number above 

7^x = 13
To solve this exponential equation you would take the log(base7) of both sides.
Log(base7)7^x=log(base7)13
The left sides reduces to x.
x = log(base7)13
Use change of base formula to solve.
x = (log13)/(log7)
x = 1.318