SOLUTION: Use the properties of logarithms to solve the given equation. log2(log2 x) = 2

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Question 957849: Use the properties of logarithms to solve the given equation.
log2(log2 x) = 2

Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Use the properties of logarithms to solve the given equation.
log2(log2 x) = 2
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log2(x) = 2^2 = 4
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x = 2^4 = 16
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Cheers,
Stan H.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
log2(log2(x)) = 2 if and only if 2^2 = log2(x).

2^2 = 4, so this becomes if and only if 4 = log2(x).

log2(x) = 4 if and only if 2^4 = x which means that x = 16.

solution is that x = 16.

equation becomes:

log2(log2(16)) = 2

you can confirm this is true by using the log conversion formula of log2(x) = log(x) / log(2)

log2(log2(16)) = 2 becomes log2(log(16)/log(2)) = 2

log(16)/log(2) = 4, so the equation becomes log2(4) = 2

log2(4) = 2 becomes log(4) / log(2) = 2 which becomes 2 = 2.

this confirms the solution is correct.