solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
2 log 4 - log 3 +2 log x - 4 = 0
A) 12.3308
B) 43.3013
C) 86.6025
D) 1875
First, use the properties of logarithms to simplify the equation:
2 log 4 - log 3 + 2 log x - 4 = 0
log 4^2 - log 3 + log x^2 - 4 = 0
log 16 - log 3 + log x^2 - 4 = 0
log(16 * x^2 / 3) - 4 = 0
log(16x^2 / 3) = 4
Now, convert to exponential form to solve for x:
10^4 = 16x^2 / 3
10000 = 16x^2 / 3
300000 = 16x^2
x^2 = 18750
x = √18750
x ≈ 136.9306
Rounded to the nearest ten-thousandth, x ≈ 136.9306
Therefore, the answer is not in the choices provided.