if lof base a 7 = 6 what is log base a^2(7)?

Answer 1

Let log_a² 7 = x
Then a^(2x) = 7
But a^6 = 7 = a^(2x)
So 2x = 6 and x = 3.

Answer 2

log (base b) N = x is equivalent to b^x = N
log (base a) 7 = 6 is equivalent to a^6 = 7.

a^6 = 7.
Take cube roots of both sides:
a^2 = 7^(1/3)

Answer 3

3

First statement means a^6 = 7

(a^2)^3 = a^6
So log a^2 (7) = 3