From the definition of logarithm:
[tex]log_b x = y[/tex] if [tex]b^y = x[/tex] (1)
The equation in our problem is:
[tex]log_{3x-2} 125 = 3[/tex]
If we use definition (1), this equation becomes
[tex](3x-2)^3 = 125[/tex]
Let's solve it:
[tex](3x-2)^3 = 5^3[/tex]
[tex]3x-2 = 5[/tex]
[tex]3x=7[/tex]
[tex]x= \frac{7}{3} [/tex]
therefore, the correct answer is C).
