olve the logarithmic equation. Round to the nearest ten-thousandth if necessary.

Question

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

Answer 1

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.