Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary. 3log 2x=4
To solve the logarithmic equation 3log(2x) = 4, we will divide both sides of the equation by 3 to isolate the logarithm.
Let's start by dividing both sides of the equation by 3:
(3log(2x))/3 = 4/3
Simplifying the left side of the equation, we have:
log(2x) = 4/3
Next, we can convert the equation from logarithmic form to exponential form. In exponential form, the base is raised to the power of the logarithm to yield the argument:
2^(4/3) = 2x
Evaluating 2^(4/3) using a calculator, we get:
2^(4/3) ≈ 2.5198
Now, we can rewrite the equation as:
2.5198 = 2x
Finally, we can solve for x by dividing both sides of the equation by 2:
2.5198/2 ≈ 1.2599
Therefore, the solution to the logarithmic equation 3log(2x) = 4 is x ≈ 1.2599.