How do you solve log(5x=6)/2=logx?

Question

It is usually shown log(5x=6)=logx
________
2

Answer 1

Let's assume you mean

[log (5x - 6)] / 2 = log x

This is

log (sqrt(5x - 6)) = log x
sqrt(5x - 6) = x
5x - 6 = x^2
x^2 - 5x + 6 = 0
(x - 3)(x - 2) = 0

x = 3; x = 2

Check:
for x = 3
[log (15 - 6)] / 2 = log(3)
log(9) / 2 = log(3)

Yes!!!

for x = 2
[log(10 - 6)] / 2 = log(2)
log(4) / 2 = log(2)

Yes!!!

Answer 2

I don't think this is a valid equation. You shouldn't have 2 "=" signs.
Check again.