Question 804807
for this problem we want to make the numbers equal.
{{{10^(x-3)=1/100}}}
we want both of the numbers to be 10.
{{{1/100=10^(-2)}}}
so we replace {{{1/100}}} with {{{10^(-2)}}}
{{{10^(x-3)=10^(-2)}}}
now you want to log both sides.
{{{log(10^(x-3))=log(10^(-2))}}}
the eponent rule with logarithms says that logx^2 = 2logx
{{{(x-3)log(10)=-2log(10)}}}
divide each side by log10
{{{x-3=-2}}}
{{{x=1}}}