Question

Log problem...will be posted below

Answer 1

\[\log_{5}n= 1/3 \log_{5}64 + 1/2 \log_{5}49 \]

Answer 2

\[\log_{5}n= \frac{1}{3} \log_{5}64 + \frac{1}{2} \log_{5}49\]\[\log_{5}n= \log_{5}64^{\frac{1}{3}} + \log_{5}49^\frac{1}{2}\]\[\log_{5}n= \log_{5}(4^3)^{\frac{1}{3}} + \log_{5}(7^2)^\frac{1}{2}\]\[\log_{5}n= \log_{5}4 + \log_{5}7\]\[\log_{5}n= \log_{5}4\times 7\]\[\log_{5}n= \log_{5}28\]\[n=...?\]

Note:
useful log properties used here:
\[(i)\ logx^m = mlogx\]\[(ii)\ logx + logy = logxy\]

Answer 3

and so 28 is the answer?

Answer 4

Yes, I think... If I haven't made any mistakes :|

Answer 5

thank you!