Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
3 log 2x = 4
(2 points)
To solve the logarithmic equation, we need to isolate the logarithm term.
First, divide both sides of the equation by 3:
log 2x = 4/3
Next, use the property of logarithms that states if log base a (b) = c, then a^c = b. In this case, the base is 10.
10^(log 2x) = 10^(4/3)
This simplifies to:
2x = 10^(4/3)
Finally, solve for x by dividing both sides of the equation by 2:
x = (10^(4/3))/2
Using a calculator, we find that x ≈ 6.3496.
Rounded to the nearest ten-thousandth, x ≈ 6.3496. Answer: \boxed{6.3496}.