olve the logarithmic equation. Round to the nearest ten-thousandth if necessary.
2 log 4 – log 3 + 2 log x – 4 = 0
(1 point)
Responses
12.3308
12.3308
43.3013
43.3013
86.6025
86.6025
1875
To solve the logarithmic equation, we can use logarithmic rules to simplify the equation and then isolate the variable x.
First, let's use the rule log(a) + log(b) = log(a * b) and log(a) - log(b) = log(a / b) to simplify the equation:
2 log 4 - log 3 + 2 log x - 4 = 0
log (4^2/3) + log (x^2) - 4 = 0
log (16/3) + log (x^2) - 4 = 0
log [(16/3) * (x^2)] - 4 = 0
log [(16/3) * (x^2)] = 4
Next, let's use the definition of logarithms to rewrite the equation:
10^4 = (16/3) * (x^2)
Now, let's solve for x:
10^4 = (16/3) * (x^2)
x^2 = (3/16) * 10^4
x^2 = 1.875 * 10^4
x^2 = 18750
Taking the square root of both sides:
x = ±√18750
Rounded to the nearest ten-thousandth, x is approximately ±43.3013.