Question

Solve the logarithmic equation algebraically. 15+2lnx=2

Answer 1

To solve the logarithmic equation algebraically, isolate the logarithm term, and then use the property of natural logarithms to solve for x. The solution to 2ln(x) = 2 is approximately x = 0.0015.

Step-by-step explanation:

To solve the logarithmic equation 15+2ln(x)=2 algebraically, we need to isolate the logarithm term. Here are the steps:

1. Subtract 15 from both sides of the equation to get 2ln(x) = -13.
2. Divide both sides by 2 to obtain ln(x) = -6.5.
3. Use the fact that the natural logarithm of a number x is the power to which e (approximately 2.7182818) must be raised to equal x. Therefore, we have x = e^(-6.5).

Using a calculator, you can evaluate x as approximately 0.0015.