RestingPlatypus
Answered

What is the solution of log3x − 12 729 = 6?

x = −5

x = −3

x = 3

x = 5


*"3x- 12" is next to log, but it's in the bottom, like an exponent, but instead of it being on top, it's below.

Verified Answer :

\(log _{3x-12} ^{729}\) = 6
\((3x-12)^{6} = 729 3x - 12 = \sqrt[6]{729} = 3 3x= 15 x=5\)

\(Domain:\\D:3x-12 > 0\ and\ 3x-12 eq1\ \ \ |add\ 12\ to\ both\ sides\\3x > 12\ and\ 3x eq13\ \ \ \ |divide\ both\sides\ by\ 3\\x > 4\ and\ x eq\frac{13}{3}\\\boxed{x\in\left(4;\ \frac{13}{3}\right)\ \cup\ \left(\frac{13}{3};\ \infty\right)}\\----------------------\\\\\log_{3x-12}729=6\\--------\\\log_ab=c\iff a^c=b\\----------\\\log_{3x-12}729=6\iff(3x-12)^6=729\\\\(3x-12)^6=3^6\iff3x-12=3\ \ \ |add\ 12\ to\ both\ sides\\3x=15\ \ \ \ |divide\ both\ sides\ by\ 3\\\boxed{\boxed{x=5\in D}}\)

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