How do you solve #log_8 25= 2log_8 x#?

1 Answer
Apr 11, 2016

#x = 5#

Explanation:

Rearrange using laws of logarithms, where a coefficient outside a #log# is the same as a power inside it.

#log_8 25 = 2log_8 x = log_8 x^2#

Raise both sides by eight,

#8^(log_8 25) = 8^(log_8 x^2)#
#25 = x^2#

which gives #x = -5, 5#.

But you can't have a #log# of a negative number, which just leaves #5#.