Question

If $5^{4a}=6^7$ and $36=5^b$, then the value of $\frac{a}{b}$ is equal to

• A. $\frac{5}{6}$
• B. $\frac{7}{8}$
• C. $\frac{4}{5}$
• D. $\frac{6}{7}$

Answer 1

The correct option is B $\frac{7}{8}$

Given: $5^{4a}=6^7$ and $36=5^b$
$36=5^b$
$\Rightarrow 6^2=5^b$
$\Rightarrow 6=(5^b{)}^{\frac{1}{2}}$
$\Rightarrow 6=5^{\frac{b}{2}}$ ....(i)
Also, $5^{4a}=6^7$
$\Rightarrow 5^{4a}={\left(5^{\frac{b}{2}}\right)}^7$ [From (i)]
$\Rightarrow 5^{4a}=5^{\frac{7b}{2}}$
$\Rightarrow 4a=\frac{7b}{2}$ $(\because a^m=a^n\Rightarrow m=n)$
$\Rightarrow 8a=7b$
$\Rightarrow \frac{a}{b}=\frac{7}{8}$
Hence, the correct answer is option (b).