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Find x, such that \(4^{\log_7x}=16\).

 Oct 15, 2019
 #1
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+1

Solve for x over the real numbers:
4^(log(x)/log(7)) = 16

Take the logarithm base 4 of both sides:
log(x)/log(7) = 2

Multiply both sides by log(7):
log(x) = 2 log(7)

2 log(7) = log(7^2) = log(49):
log(x) = log(49)

Cancel logarithms by taking exp of both sides:
x = 49

 Oct 15, 2019
 #2
avatar+104969 
+1

Here's a slightly shorter approach

 

Note that 4^2  = 16

 

Which must mean that

 

log 7 x  =  2

 

So....in exponential form    7^2  = x   =  49

 

 

cool coolcool

 Oct 15, 2019

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