Question

What is the solution of log3x - 12 729 = 6? the 3x-12 is like lower than log

Answer 1

\(\huge log_{3x - 12}(729) = 6\quad ?\)

Answer 2

yes like that

Answer 3

\[\Large \log_{3x - 12} 729 = 6\]\[\Large \log_{B} A = C\]means\[\Large A = B^{C}\]

Answer 4

hmm you know the change of base rule, right?

Answer 5

\[\Large \log_{3x - 12}(729) = 6\quad means \quad (3x - 12)^{6} = 729\]

Answer 6

729 = 3^6
Solve for x.

Answer 7

uhm so like distribute th e6 to the 3x and the 12?

Answer 8

\[\Large (3x - 12)^{6} = 729 = 3^{6}\]. Both are raised to 6. Therefore, 3x - 12 = 3.
Solve for x.

Answer 9

so it would be 5?

Answer 10

Yes, x = 5.

Another way to look at it is: (3x - 12)^6 = 729
Find the sixth root on both sides (that is, raise both sides to the power 1/6):
3x - 12 = 729^(1/6) = 3