Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.

Question

3 log 2x = 4

(2 points)

Answer 1

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}.