matthewe1903 matthewe1903
  • 23-04-2018
  • Mathematics
contestada

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

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skyluke89
skyluke89 skyluke89
  • 05-05-2018
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).
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