Question

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.

Answer 1

`log _(3x-12) ^(729)` = 6

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

Answer 2

`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(13)/(3)\\\boxed{x\in\left(4;\ (13)/(3)\right)\ \cup\ \left((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}}`