Question 154537
If log base 8 of 3=r and log base 8 of 5=s, express log base 8 of 3/64 in terms of r and s.

If {{{log(8,3)=r}}} and {{{log(8,5)=s}}}, express {{{log(8,(3/64))}}} in terms of r and s.
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{{{log(8,(3/64))}}}

Use this logarithm rule:  {{{log(B,(A/C))=log(B,A)-log(B,C)}}}

{{{log(8,(3/64))=log(8,3)-log(8,64)}}}

Write {{{64}}} as {{{8^2}}}

{{{log(8,(3/64))=log(8,3)-log(8,8^2)}}} 

Use this logarithm rule on the last term: {{{log(B,A^C)=C*log(B,A)}}}

{{{log(8,(3/64))=log(8,3)-2*log(8,8)}}}

Then use this logarithm rule on the last term: {{{log(B,B)=1}}}

{{{log(8,(3/64))=log(8,3)-2*1}}}

{{{log(8,(3/64))=r-2}}}

s was not needed.

Edwin</pre>