Solve ln 3 + ln (4x) = 4. Round your answer to the nearest hundredth.
A.
0.01
B.
0.91
C.
4.55
D.
12.90
x=4.55
To solve ln 3 + ln (4x) = 4, we can use the properties of logarithms.
Step 1: Combine the logarithms using the product rule of logarithms.
ln 3(4x) = 4
Step 2: Simplify the expression.
ln (12x) = 4
Step 3: Convert the equation into exponential form.
e^4 = 12x
Step 4: Solve for x by dividing both sides by 12.
x = e^4/12
Using a calculator to evaluate e^4/12, we get x ≈ 4.59.
Rounding to the nearest hundredth, x ≈ 4.59 ≈ 4.55.
Therefore, the answer is C. 4.55.
To solve the equation ln 3 + ln (4x) = 4, we can use the properties of logarithms.
First, we can rewrite the equation using the property of logarithms which states that the sum of logarithms is equal to the logarithm of the product. Therefore, ln 3 + ln (4x) can be rewritten as ln (3 * 4x).
Now, using another property of logarithms which states that ln (a * b) = ln a + ln b, we can simplify ln (3 * 4x) to ln 12x.
So now, the equation becomes ln 12x = 4.
To solve for x, we need to isolate the variable by getting rid of the natural logarithm. We can do this by exponentiating both sides of the equation with base e (the base of the natural logarithm).
Therefore, we have e^(ln 12x) = e^4.
The exponential function e^x and the natural logarithm ln x are inverse functions, so they cancel each other out. This leaves us with 12x = e^4.
Finally, we solve for x by dividing both sides of the equation by 12:
x = (e^4) / 12.
To find the approximate value of x, we can use a calculator or a computer program to evaluate this expression:
x ≈ 12.90 (rounded to the nearest hundredth).
So the correct answer is D. 12.90.
except for the lx part, this is just algebra I
3 + ln (4x) = 4
ln(4x) = 1
Now, get rid of the ln by doing its inverse: e^
4x = e^1
x = e/4