Question

if \[\log_{9}4=a\]and \[\log_{27}5=b\] find an expression in terms of a & b for \[\log_{3}80\]

Answer 1

i had that backwards
\[2\log_9(4)=\log_3(4)\] and
\[3\log_{27}(5)=\log_3(5)\] now lets see what we can do with \(\log_3(80)\)

Answer 2

since \(80=4^2\times 5\) we can write
\[\log_3(80)=\log_3(4^2\times 5)=\log_3(4^2)+\log_3(5)=2\log_3(4)+\log_3(5)\]

Answer 3

now substitute back for \(a\) and \(b\) and you will get your answer

Answer 4

this is how they explained for me to do it...so im sort of just going by this.
lookin at what you did... im gettng a little lost... /: