3ˣ = x⁹ | Find the Value of x | 99% Students Failed This Question 😱

Solution: Solve 3^x = x⁹

Given:

3^x = x⁹

Taking logarithm on both sides:

log(3^x) = log(x⁹)

Using log properties:

x log 3 = 9 log x

Dividing by x:

log 3 = 9 log(x^1/x)

log(x^1/x) =1/9(log3) 

log(x^1/x) =(log3^1/9) 

Hence,

x^1/x = 3^1/9

Checking x = 27:

3²⁷ = (3³)⁹ = 27⁹

Therefore,

x = 27