What is the solution to 2log5x = log54?

Log5 (x^2) - log5 (x) = log5 (3) + log5 (4), which is:

The solution

Translate the equation first

log5 (x^2/x) = log5 (3*4),

x^2/x = 12

x^2 = 12x

x^2 - 12x = 0

x (x - 12) = 0

x = 0, 12, while, x = 0

We have the following expression:

2log5x = log54

Rewriting we have:

2log5x = 0.861353116

log5x = 0.861353116 / 2

log5x = 0.430676558

We clear the value of x:

5 ^ (log5x) = 5 ^ (0.430676558)

x = 5 ^ (0.430676558)

x = 2

Answer:

the solution to 2log5x = log54 is:

x = 2