Solve the equation below. Round your answer to the nearest hundredth. ln3+ln(4x)=4

Question

Responses
0.01
12.90
4.55
0.91

Answer 1

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.