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  4. If ( log a/5)=( log b/6)=( log c/7), then b2=

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Q. If $\frac{\log a}{5}=\frac{\log b}{6}=\frac{\log c}{7}$, then $b^2=$

Logarithms

Solution:

Let $\frac{\log a}{5}=\frac{\log b}{6}=\frac{\log c}{7}=k$
$\Rightarrow \log a=5 k $
$ \Rightarrow a=10^{5 k} $
$ \log b=6 k $
$ \Rightarrow b=10^{6 k } $
$ \log c=7 k $
$ \Rightarrow c=10^{7 k} $
$ b^2=(10^{6 k })^2=10^{12 k } $
$ =10^{7 k } \times 10^{5 k }=a c$