Question

If $\frac{{25}^x\times {10}^{2x}}{4^x}=5^8$, find $x$.

Answer 1

$\frac{{25}^x\times {10}^{2x}}{4^x}=5^8$

$\Rightarrow \frac{5^{2x}\times 2^{2x}\times 5^{2x}}{2^{2x}}=5^8$

$\Rightarrow 5^{4x}\times 2^{2x-2x}=5^8$

$\Rightarrow 5^{4x}\times 2^0=5^8$

$\Rightarrow 5^{4x}=5^8$

Since bases are same, we can equate the powers.

$\Rightarrow 4x=8$

$\therefore x=\frac{8}{4}=2$