Express lnx Squareroot 1 x2 in terms of sums andor differen

Express ln(x Squareroot 1 + x^2) in terms of sums and/or differences of simple logarithms. A. ln x - 1/2 ln (1 + x^2) B. 1/2 ln x + 1/2 ln (1 + x^2) C. ln x + ln (1 + x) D. ln x - ln (1 + x) E. ln x + 1/2 ln (1 + x^2) Solve the exponential equation: 2e^3x = 10 A. x = ln (5)/3 B. x = 10/2e^3 C. x = log_2e(10)/3 D. x = ln (10)/ln (2e) E. x = e^5/3

Solution

49) ln (x * (1 + x²)^1/2) = ln x + ln ( (1 + x²)^1/2)

                                  = ln x + 1/2 * ln (1 + x²)

Option-D)

50) 2e^3x = 10

or, e^3x = 5

or, 3x = ln 5

or, x = ln(5) / 3

Option-A)