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 Question from Iriogbe: Find the value : if log3 (a-6) =2b and log2 (a-7) =3b

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

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