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, divide both sides of the equation by 3:
log 2x = 4/3
Next, rewrite the equation in exponential form. In exponential form, log base b of a is equivalent to b raised to the power of the logarithmic expression equals a:
2x = 10^(4/3)
To solve for x, take the logarithm of both sides to the base 2:
log base 2 (2x) = log base 2 (10^(4/3))
x = log base 2 (10^(4/3)) / log base 2 (2)
Using a calculator, where log base 2 = ln with the base divided by ln 2:
x ≈ 5.0397.