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

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

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