SOLUTION: Change to logarithmic form: 0.125=2^-3

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Question 169332: Change to logarithmic form: 0.125=2^-3
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
if y+=+x%5En
then log%28x%2Cy%29+=+n
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let y = .125
let x = 2
let n = -3
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your equation becomes:
log%282%2C%28.125%29%29+=+-3
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to prove this is correct, translate to base 10 and solve on calculator.
translation formula is:
log%28x%2Cy%29 = %28log%2810%2Cy%29%29%2F%28log%2810%2Cx%29%29 = n
when x = 2, and y = .125, and n = -3, this formula becomes:
log%282%2C%28.125%29%29 = %28log%2810%2C%28.125%29%29%29%2F%28log%2810%2C2%29%29 = -3 = n
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solving on the calculator yields n = -3 which is correct.
basic equation for exponents and logarithms is:
y+=+x%5En if and only if log%28x%2Cy%29+=+n