Question

(81)⁵/× = 243
find value of x

Answer 1

$81^{ \frac{5}{x} }=243\\ \\ \Rightarrow (3^4)^{ \frac{5}{x} }=3^5\\ \\ \Rightarrow (3)^{ \frac{4 \times 5}{x} }=3^5\\ \\ \Rightarrow 3^{ \frac{20}{x} }=3^5$

Comparing the powers, 

$\frac{20}{x} =5\\ \\x= \frac{20}{5} =\boxed4$