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
To solve the logarithmic equation, we can combine the logarithms using the properties of logarithms.
2 log 4 – log 3 + 2 log x – 4 = 0
Using the quotient rule of logarithms (log a - log b = log(a/b)), we can combine the first two terms:
log(4^2/3) + 2 log x – 4 = 0
Simplifying the exponent of 4^2/3:
log(16/3) + 2 log x – 4 = 0
Using the product rule of logarithms (log a + log b = log(ab)), we can combine the second and third terms:
log(16/3) + log(x^2) – 4 = 0
Applying the power rule of logarithms:
log(16/3) + log(x^2) – log(10^4) = 0
Using the product rule again:
log[(16/3) * x^2 / 10^4] = 0
Setting the inside of the logarithm equal to 1:
(16/3) * x^2 / 10^4 = 1
Multiplying both sides by 10^4 to eliminate the fraction:
(16/3) * x^2 = 10^4
Dividing both sides by (16/3):
x^2 = (10^4)(3/16)
Taking the square root of both sides:
x = sqrt((10^4)(3/16))
Calculating the value of x using a calculator:
x ≈ 43.3013
Rounding to the nearest ten-thousandth:
x ≈ 43.3013
Therefore, the correct answer is B) 43.3013.
Yay, you did it... But you got me a 2/5 on the assignment.
Real answers:
1. 3/16
2. 0.3281
3. 1.31
4. 96 hours
5. 43.3013
100% correct
Keep hanging on,
don't let go.
-Mortis