Hi,

I think you are to find the value of $b.$

I would rather work with exponential expressions than with logarithms so I am going to use

\[\log_3(a-6) = 2b \mbox{ is equivalent to } 3^{2b} = a-6\]

and

\[\log_2(a-7) = 3b \mbox{ is equivalent to } 2^{3b} = a-7\]

Hence you have

\[9^b = a-6 \mbox{ and } 8^b = a-7\]

Can you complete it now?
Penny