SOLUTION: solve 10^(x-3)=1/100 using logarithms

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Question 804807: solve 10^(x-3)=1/100 using logarithms
Found 2 solutions by erica65404, stanbon:
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
for this problem we want to make the numbers equal.
10%5E%28x-3%29=1%2F100
we want both of the numbers to be 10.
1%2F100=10%5E%28-2%29
so we replace 1%2F100 with 10%5E%28-2%29
10%5E%28x-3%29=10%5E%28-2%29
now you want to log both sides.
log%2810%5E%28x-3%29%29=log%2810%5E%28-2%29%29
the eponent rule with logarithms says that logx^2 = 2logx
%28x-3%29log%2810%29=-2log%2810%29
divide each side by log10
x-3=-2
x=1

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve 10^(x-3)=1/100 using logarithms
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Take the log of both sides::
(x-3)log(10) = log(10^(-2))
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(x-3) = -2
x = 1
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Cheers,
Stan H.
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