\log_8 a + \log_4 b^2 = 5,\quad \log_8 b + \log_4a^2 = 7
Find ab.
\log_8(a)+\log_4(b^2)=5
\log_8(b)+\log_4(a^2)=7
\frac{1}{3}\log_2(a)+\log_2(b)=5 (1)
\frac{1}{3}\log_2(b)+\log_2(a)=7 (2)
sum of (1) and (2)
\frac{4}{3}\log_2(b)+\frac{4}{3}\log_2(a)=12
\log_2(b)+\log_2(a)=\log_2(ab)=9
ab=2^9=512
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