Log rule confusion during : Log = 1 + Log

Question

Log₅(x²) = 1 + Log₅(6)

1. Uses rule a=log_b(b^a) to get log₅(x²) = log₅(30)
2. x²= 30
3. x = square of 30

There is nothing online about “1 + logarithms” and when there is they expotentate. Why is this rule used? Everything is easy except for when it is explained as “log₅(5^1+log₅⁽⁶⁾)” which somehow equals 30

Answer 1

Answer 2

note that log5(5) = 1 so

log5(x^2) = log5(5) + log5(6)

5^log5(x^2) = 5^log5(5) * 5^log5(6)

x^2 = 30

x = sqrt(30)