Question

The solution of ${64}^{2x-5}=4\times 8^{x-5}$ is

• A. $\frac{9}{17}$
• B. $\frac{17}{9}$
• C. $\frac{17}{10}$
• D. $\frac{20}{9}$

Answer 1

The correct option is B $\frac{17}{9}$

The given equation is ${64}^{2x-5}=4\times 8^{x-5}$

$\Rightarrow 2^{6(2x-5)}=2^2.2^{3(x-5)}$

$\Rightarrow 2^{12x-30}=2^{2+3x-15}$

As the bases are same, powers must be equal.

Thus, $12x-30=3x-13$

$\Rightarrow 12x-3x=-13+30$

$\Rightarrow x=\frac{17}{9}$