Question

Solve for x and express your answer as a logarithm.

2(10^(3x) ) = 24


Simplify your answer as much as possible.


Use the following notations where necessary:

• For fractions, use the / symbol to separate numerator and denominator, like this: 42/53

• For logs with a base of 10, such as log107, just write the log without the base and place the value in parentheses, like this: log(7)

• For logs with a base other than 10, write the base after an underscore then place the value in parentheses. For example, to write log27, write it like this: log_2(7)

Answer 1

`2\cdot10^(3x)=24\ \ \ \ |divide\ both\ sides\ by\ 2\\\\10^(3x)=12\iff\log(10^(3x))=\log(12)\\\\3x\log(10)=\log(12)\\\\3x=\log(12)\ \ \ \ |divide\ both\ sides\ by\ 3\\\\\boxed{x=(\log(12))/(3)}\to(\log(12))/(3)=(1)/(3)\log(12)=\log\left(12^(1)/(3)\right)=\boxed{\log\sqrt[3]{12}}`


`Use:\\\log_ab^c=c\log_ab\\\log_aa=1\\a^(1)/(n)=\sqrt[n]{a}\\-------------------\\\\Answer:\boxed{x=(\log(12))/(3)\ other\ form\ x=\log(\sqrt[3]{12})}`