Question

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

• A. $ac$
• B. $a^2$
• C. $ab$
• D. $bc$

Answer 1

Answer: (A)

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