SOLUTION: How do I solve the equation for x: 64=2^3^x?

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Question 175148: How do I solve the equation for x: 64=2^3^x?
Found 2 solutions by Earlsdon, solver91311:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
64+=+%282%5E3%29%5Ex Substitute 2%5E3+=+8
64+=+8%5Ex Substitute 64+=+8%5E2
8%5E2+=+8%5Ex The bases (8) are equal so the exponents are equal.
x+=+2

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
I think you mean: 64=2%5E3%5Ex

Recognize that 64 is a power of 2, namely 64=2%5E6. Hence, 2%5E6=2%5E3%5Ex and therefore 3%5Ex=6

Take the log of both sides:

log%28%283%5Ex%29%29=log%28%286%29%29

But we know that log%28%28r%5Es%29%29=s%2Alog%28%28r%29%29, so:

x%2Alog%28%283%29%29=log%28%286%29%29 and finally,

x=log%28%286%29%29%2Flog%28%283%29%29 which is the exact answer. Use your calculator for a numerical approximation of the appropriate precision if necessary.