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

Question

jdoe0001 · Answer

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

anonymous · Answer

yes like that

ranga · Answer

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

jdoe0001 · Answer

hmm you know the change of base rule, right?

ranga · Answer

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

ranga · Answer

729 = 3^6
Solve for x.

anonymous · Answer

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

ranga · Answer

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

anonymous · Answer

so it would be 5?

ranga · Answer

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