What is the solution?

Question

What is the answer for
Given that : log_5 x = 4log_x 5 Find x
The answers is 1/25 and 5 but the working.........

Answer 1

(log base 5) x = 4 (log base x) 5
(log base 5) x = (log base x) 5^4
(log base 5) x = (log base x) 625

Change to base 5.

(log base 5) x = (log base 5) 625 / (log base 5) x
[ (log base 5) x ]^2 = (log base 5) 5^4
[ (log base 5) x ]^2 = 4

(log base 5) x = 2 or (log base 5) x = -2
x = 25 or x = 1/25

Answer 2

Your way of writing the problem is somewhat ambiguous. This should be resolved by judicious use of parentheses to make clear what you are saying.

Assume that your problem is:
log(5x) = 4log(x5) = 4 log (5x) = log{ (5x)**4}
or 5x = (5x)**4
1 = (5x)**3 = 125x**3 or [cuberoot of (1/125)] = x = 1/5

Answer 3

rewrite
5^x = x^(4*5)
now solve before someone from india gets the high paying job you should have