Question 411337: (log4(log4 x))=−2
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! (log4(log4 x))=−2
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(log4(log4 x))=−2
Definition of logarithm: The base raised to the logarithm of a number is equal to the number. To solve the given problem we will do it in two steps. In the first step,the base=4, the logarithm of the number=-2, and the number is log4x. The second step follows the same definition.
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first step:
4^-2=log4x
1/4^2=log4x
1/16=log4x
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second step
4^(1/16)=x
x=1.0905
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check: using log base 10 on calculator and change-of-base formula
(log4(log4 x))=−2
log4x=log4(1.0905)=log(1.0905)/log(4)=.06249
log4(.06249)=log(.06249)/log(4)=-2.000..
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