Solve log2(log8(x)) = log8(log2(x)).
Because 23 = 8, I'm wondering if changing bases might help? thank you for your advice.
I think you're on the right track. Use the change-of-base formula
to convert everything to base-2:
Using another log rule
, you get:
(x) = 0, so x = 1, or (log2
= 27, log2
(x) = sqrt, so x = 2 sqrt
Comparing with the original expressions, you can't have x = 1, because then log2
(x) = 0, but you can't take log8
(1)) = log8
Whew! I'll leave the check of the other solution value to you.