How to solve the following equation? log_3(log_x(log_4 16))=−1.

raapjeqp 2022-10-23 Answered
How to solve the following equation? log 3 ( log x ( log 4 16 ) ) = 1
I am trying to solve this equation for x. This is what I have so far:
log 3 ( log x 2 ) = 1.
Okay, now I have this:
log 2 = ( 1 / 3 ) log x
How do I isolate x from here?
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Answers (2)

Aidyn Mccarthy
Answered 2022-10-24 Author has 12 answers
Adriano's method is another method, I will continue where you stopped:
log 3 ( log x 2 ) = 1 1 3 = log x ( 2 )
by the definition of the logarithm.
Now x 1 / 3 = 2 x = 2 3 = 8, again by the definition of the logarithm.
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Danika Mckay
Answered 2022-10-25 Author has 5 answers
Hint: There is no multiplication going on anywhere in this equation (just nested logs). Try thinking of the stuff inside the brackets as a single unit and convert to exponential form, working your way from the outside to the inside. If it helps, use substitutions. For example, let u = log x ( log 4 16 ) ), so that we have:
log 3 u = 1
Converting to exponential form, we have:
u = 3 1 log x ( log 4 16 ) = 1 3
Now repeat.
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