Question

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

Answer 1

$Domain:\\D:3x-12 > 0\ and\ 3x-12\neq1\ \ \ |add\ 12\ to\ both\ sides\\3x > 12\ and\ 3x\neq13\ \ \ \ |divide\ both\sides\ by\ 3\\x > 4\ and\ x\neq\frac{13}{3}\\\boxed{x\in\left(4;\ \frac{13}{3}\right)\ \cup\ \left(\frac{13}{3};\ \infty\right)}\\----------------------\\\\\log_{3x-12}729=6\\--------\\\log_ab=c\iff a^c=b\\----------\\\log_{3x-12}729=6\iff(3x-12)^6=729\\\\(3x-12)^6=3^6\iff3x-12=3\ \ \ |add\ 12\ to\ both\ sides\\3x=15\ \ \ \ |divide\ both\ sides\ by\ 3\\\boxed{\boxed{x=5\in D}}$

Answer 2

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