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

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

Algebra 2

x ≈ ±20.086/√ (t - 1)

Step-by-step 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)