Question

Solve this equation 4log√x - log 3x =log x^2​

Answer 1

`x = (1)/(3)`

Explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒(
`(1)/(3x)`)

*rewrite to solve for x :

10⁰ =
`(1)/(3x)`

1 =
`(1)/(3x)`

1 · x =
`(1)/(3x)` · x

1x =
`(1)/(3)`

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x =
`(1)/(3)`