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Solve the equation \(\log_3 (\log_2 x) = 2 \)

 Mar 2, 2018
 #1
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+1

Solve for x:

log(log(x)/log(2))/log(3) = 2

 

Multiply both sides by log(3):

log(log(x)/log(2)) = 2 log(3)

 

2 log(3) = log(3^2) = log(9):

log(log(x)/log(2)) = log(9)

 

Cancel logarithms by taking exp of both sides:

log(x)/log(2) = 9

 

Multiply both sides by log(2):

log(x) = 9 log(2)

 

9 log(2) = log(2^9) = log(512):

log(x) = log(512)

 

Cancel logarithms by taking exp of both sides:

 

x = 512

 Mar 2, 2018
 #2
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Log(x) / Log(2) = 3^2, solve for x

Log(x) = 9log(2)

Log(x) = log(2^9)

x = 512

 Mar 2, 2018

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