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 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.