Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
3 log 2x = 4
To solve the logarithmic equation 3 log 2x = 4, we need to isolate the logarithm first.
First, divide both sides by 3 to get log 2x = 4/3.
Next, we can rewrite the logarithmic equation in exponential form to solve for x. Remember that log base a (x) = y can be written as a^y = x. So, in this case, 2^(4/3) = 2x.
2^(4/3) = 2x
8^(1/3) = 2x
2 = 2x
x = 1
Therefore, the solution to the logarithmic equation 3 log 2x = 4 is x = 1.