Solve the equation below. Round your answer to the nearest hundredth. ln3+ln(4x)=4
Responses
0.01
12.90
4.55
0.91
To solve the equation ln3 + ln(4x) = 4, we can use the properties of logarithms.
First, we can combine the logarithms by using the product property of logarithms:
ln(3 * 4x) = ln(12x)
The equation now becomes:
ln(12x) = 4
Next, we can convert the logarithmic equation into an exponential equation:
e^4 = 12x
Simplifying further:
54.6 = 12x
Finally, we can solve for x:
x = 54.6 / 12
x ≈ 4.55
Rounding to the nearest hundredth, the solution to the equation is approximately 4.55. Therefore, the correct response is 4.55.