Question 172047
Close, but no cigar this time.


{{{log((z^2-25))-log((z+5))=log((7))}}}


Remember the rules:


The sum of the logs is the log of the PRODUCT.


The difference of the logs is the log of the QUOTIENT.


So you should have written:


{{{log(((z^2-25)/(z+5)))=log((7))}}}


From here you should be able to recognize that {{{z^2-25=(z+5)(z-5)}}} so {{{log(((z^2-25)/(z+5)))= log((z-5)) = log((7))}}}


Furthermore, {{{log(b,(a))=log(b,(c))}}} if and only if {{{a=c}}}, so:


{{{z-5=7}}}


{{{z=12}}}