document.write( "Question 804807: solve 10^(x-3)=1/100 using logarithms \n" ); document.write( "

Algebra.Com's Answer #484954 by erica65404(394) $\"\"$ $\"About$

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for this problem we want to make the numbers equal.
\n" ); document.write( " $\"10%5E%28x-3%29=1%2F100\"$
\n" ); document.write( "we want both of the numbers to be 10.
\n" ); document.write( " $\"1%2F100=10%5E%28-2%29\"$
\n" ); document.write( "so we replace $\"1%2F100\"$ with $\"10%5E%28-2%29\"$
\n" ); document.write( " $\"10%5E%28x-3%29=10%5E%28-2%29\"$
\n" ); document.write( "now you want to log both sides.
\n" ); document.write( " $\"log%2810%5E%28x-3%29%29=log%2810%5E%28-2%29%29\"$
\n" ); document.write( "the eponent rule with logarithms says that logx^2 = 2logx
\n" ); document.write( " $\"%28x-3%29log%2810%29=-2log%2810%29\"$
\n" ); document.write( "divide each side by log10
\n" ); document.write( " $\"x-3=-2\"$
\n" ); document.write( " $\"x=1\"$ \n" ); document.write( "

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