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:
$(3x-2)^3 = 5^3$
$3x-2 = 5$
$3x=7$
$x= \frac{7}{3}$

therefore, the correct answer is C).