precal question

Question

Consider the following.

5^3x − 1 = 6

(a) Find the exact solution of the exponential equation in terms of logarithms.

x = 

Answer 1

Take log base 5 of both sides to get:

log₅(5^{3x − 1}) = log₅(6) then use the property of logs that brings an exponent out front to get:

(3x - 1)log₅(5) = log₅(6)

(3x - 1)(1) = log₅(6)

3x = log₅(6) + 1

x = (log₅(6) + 1)/3