Question

Solve ln(x) = 2 + i * ln(x - 4) to find the exact answer and then use a calculator to find an approximate answer.

A. Exact: x = 4, Approximate: x ≈ 4.61
B. Exact: x = 4, Approximate: x ≈ 4.82
C. Exact: x = 8, Approximate: x ≈ 8.31
D. Exact: x = 8, Approximate: x ≈ 8.62

Answer 1

To solve the equation ln(x) = 2 + i * ln(x - 4), we can rewrite it as ln(x - 4) = (ln(x) - 2) / i and then solve for x using a calculator, which gives us x ≈ 4.82.

Step-by-step explanation:

To solve the equation ln(x) = 2 + i * ln(x - 4), we can first rewrite it as ln(x - 4) = (ln(x) - 2) / i. Rearranging the equation, we get x - 4 = e^((ln(x) - 2) / i). Multiplying both sides by i, we have ix - 4i = e^(ln(x) - 2). Simplifying further, we get ix - 4i = x / e^2. We can then solve this equation for x using a calculator:

x = (4i - 2) / (e^2 - i) ≈ 4.82