How to solve the equation 13^(3x-1)=15?the result is expected to have up to 4 decimals

To solve for x, we'll have to take natural logarithms both
sides:

ln 13^(3x-1) = ln
15

We'll use the power rule of
logarithms:

(3x-1)*ln 13 = ln
15

We'll divide by ln 13 both sides of the
equation:

(3x-1) = ln 15 /ln
13

We'll add 1  both sides:

3x
= ln 15 /ln 13 + 1

We'll divide by
3:

x = (ln 15 /ln 13 + 1)/3

x
= (ln 15 + ln 13)/3*ln 13

x = ln (15*13)/ln
13^3

We'll evaluate the numerator of the
fraction:

ln (15*13) =
5.2729

We'll evaluate the denominator of the
fraction:

ln 13^3 = 7.6948

x =
5.2729/7.6948

x =
0.6852

The requested soution of the equation,
rounded up to 4 decimals, is x = 0.6852.