Question

Solve the equation. Check your answer. If necessary, round to 3 decimal places

In (t - 1) + In x^2 = 6, X=

Algebra 2

Answer 1

x ≈ ±20.086/√(t - 1)

Explanation:

ln(t - 1) + ln(x²) = 6

Recall that lnu + lnv = ln(uv). Then

ln(t - 1) + ln(x²) = ln[(t-1)x²] = 6

Take the natural antilogarithm of each side

(t - 1)x² = e⁶

Divide each side by t - 1

x² = e⁶/(t-1)

Take the square root of each side

x = ±e³/√(t - 1)

x ≈ ±20.086/√(t - 1)