Solve each equation Approximate your answer to 4 decimal pla

Solve each equation. Approximate your answer to 4 decimal places. e^- x^3 = e^x^2 - 2x 4(3^x) = 48 7 - 2e^x = 5 ln x - 7 = 0 ln(x + 5) = ln(x - 1) - ln(x + 1) log_3 x + log_3 (x - 8) = 2

Solution

a) –x^2 = x^2 – 2x ===========> 2x^2 – 2x = 0

x = 0, 1

b) 3^x = 12

     x*ln3 = ln 12

    x = ln12/ln3 = 2.262

c) 7 – 2e^x = 5

    2e^x = 2

   e^x = 1 ========> x = 0

d) ln x – 7 = 0 ======> ln x = 7 ======> x = 1096.63

e) ln(x + 5) = ln(x - 1) – ln(x + 1)

    x + 5 = (x - 1)/(x + 1)

    x^2 + 6x + 5 = x – 1

    x^2 + 5x + 6 = 0

   x = -2, -3