Question

If $2^{5x}÷2^x=5\sqrt{20}.$ Find $x$

Answer 1

$2^{5^x}÷2^x=5\times 2\times \sqrt{5}$

$2^{4x}=5^{3/2}\times 2$

$4x\log 2=\frac{3}{2}\log 5+\log 2$

$x=\frac{\frac{3}{2}\log 5+\log 2}{4\log 2}$

$x=1.12$