solving log_2(log_8(x)) = log_8(log_2(x))  TOPIC_SOLVED

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solving log_2(log_8(x)) = log_8(log_2(x))

Postby maggiemagnet on Mon May 18, 2009 5:26 pm

Solve log2(log8(x)) = log8(log2(x)).

Because 23 = 8, I'm wondering if changing bases might help? thank you for your advice.
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  TOPIC_SOLVED

Postby stapel_eliz on Fri May 22, 2009 5:48 pm

maggiemagnet wrote: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:



...so:



Also:



Using another log rule, you get:





Then:











Then log2(x) = 0, so x = 1, or (log2(x))2 = 27, log2(x) = sqrt[27], so x = 2 sqrt[27].

Comparing with the original expressions, you can't have x = 1, because then log2(x) = 0, but you can't take log8(log2(1)) = log8(0).

Whew! I'll leave the check of the other solution value to you. :shock:
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Re: solving log_2(log_8(x)) = log_8(log_2(x))

Postby maggiemagnet on Sat May 23, 2009 12:45 pm

Goodness! Now I don't feel so bad about bogging down!

Thank you so much! :clap:
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