Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary. 3 log 2x = 4

Answer 1

To solve the logarithmic equation 3 log 2x = 4, we need to first isolate the logarithm by dividing both sides by 3:

log 2x = 4/3

Next, we can rewrite the equation in exponential form:

2^(4/3) = 2x

2^(4/3) = 2x

2^(4/3) = 2x

Taking the cube root of both sides, we get:

2^(4/3) = x

Thus, x = 2^(4/3), which simplifies to x = 2.5198 (rounded to four decimal places).

Therefore, the solution to the logarithmic equation 3 log 2x = 4 is x = 2.5198.