SOLUTION: How do I solve the equation 4^2X=64? The teacher gave us the answer, 3/2, but I don't know the steps to get to that answer.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do I solve the equation 4^2X=64? The teacher gave us the answer, 3/2, but I don't know the steps to get to that answer.      Log On


   

Question 673067: How do I solve the equation 4^2X=64? The teacher gave us the answer, 3/2, but I don't know the steps to get to that answer.
Found 3 solutions by mananth, Alan3354, MathLover1:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
4^2X=64
2x log 4 = log 64
2x= log 64/log4
2x=3
x= 3/2

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How do I solve the equation 4^2X=64? The teacher gave us the answer, 3/2, but I don't know the steps to get to that answer.
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4%5E%282x%29+=+64
%282%5E2%29%5E%282x%29+=+64
2%5E%284x%29+=+64+=+2%5E6
4x = 6
x = 3/2
That's one way.
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4%5E%282x%29+=+64+=+4%5E3
2x = 3, etc
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4%5E%282x%29+=+64
2x*log(4) = log(64)
x+=+log%2864%29%2F%282log%284%29%29
x = 3/2

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

4%5E%282x%29=64
4%5E%282x%29=4%5E3........if base same, exponents are same too; so, we have
2x=3
x=3%2F2