Final answer:
To solve the equation 4 - 3ln(2x + 10) = 12, first isolate the ln term, exponentiate to solve for x, and then enter the result into a calculator, rounding to two decimal places. The solution is approximately x ≈ 2.20.
Step-by-step explanation:
To solve the equation 4 - 3ln(2x + 10) = 12, let's begin by isolating the natural logarithm on one side. First, subtract 4 from both sides:
4 - 3ln(2x + 10) - 4 = 12 - 4
-3ln(2x + 10) = 8
Now, divide by -3 to get:
ln(2x + 10) = -8 / -3
ln(2x + 10) = 8 / 3
Next, we exponentiate both sides to remove the natural logarithm:
e^(ln(2x + 10)) = e^(8 / 3)
2x + 10 = e^(8 / 3)
Now, subtract 10 from both sides:
2x = e^(8 / 3) - 10
Finally, divide by 2 to solve for x:
x = (e^(8 / 3) - 10) / 2
Enter your data into a calculator and round to two decimal places:
x ≈ (e^(2.67) - 10) / 2
x ≈ (14.39 - 10) / 2
x ≈ 4.39 / 2
x ≈ 2.20