Question

What is the solution of log 3(x - 2)125 = 3 ? Choose one answer. a. x = 1 over 3 b. x = 1 c. x = 7 over 3 d. x = 4

Answer 1

From the definition of logarithm:

`log_b x = y` if
`b^y = x` (1)

The equation in our problem is:

`log_(3x-2) 125 = 3`
If we use definition (1), this equation becomes

`(3x-2)^3 = 125`

Let's solve it:

`(3x-2)^3 = 5^3`

`3x-2 = 5`

`3x=7`

`x= (7)/(3)`

therefore, the correct answer is C).