RestingPlatypusidn
Answered

Join the IDNLearn.com community and get your questions answered by experts. Ask anything and receive well-informed answers from our community of experienced professionals.

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.

Sagot :

[tex]log _{3x-12} ^{729} [/tex] = 6
[tex](3x-12)^{6} = 729 3x - 12 = \sqrt[6]{729} = 3 3x= 15 x=5[/tex]
[tex]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}}[/tex]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.