Can I please get help on the HIGHLIGHTED QUESTIONS only Than

Can I please get help on the HIGHLIGHTED QUESTIONS only? Thanks. 3

Evaluate the expression using a calculator. Give answers accurate to five decimal places. In 15.2 12 log 110 log(2/3) ln Squareroot 21 log(2 Squareroot 3) In (17/5) (In 0.41)^3 log(3.52 times 10^47) Evaluate the expression without the use of a calculator. log_2 16 log_3 1/9 log_3 0 log_23 1 ln e^2 log 10,000 log_5 1/216 log_7 343 log_1/5 25 log_3/4 (4/3)^100 log_0.1 1000 log_Squareroot 2 16 log (10^100) ln Squareroot e ln (e^4 middot e^3) log (10^4 middot 10^-3) Use a graphing calculator to estimate the value of the expression to the nearest hundredth. Log_5 37 log_2 12 log_2 50 log_100 8 log_1/2 108 log_1/3 11 Write an exponential equation equivalent to the given logarithmic equation. log_2 1/4 = -2 log_1/3 9 = -2 log 1000 = 3 ln 7 = x ln (x + 1) = 2 log x = 4 log_x 10 = 3 ln (3x +1) = x Write a logarithmic equation equivalent the given exponential equation.

Solution

11. ln 15.2 = 2.721295 = 2.72130( on rounding off to 5 decimal places)

15. log (23)=log2+log3 =log 2+ log( 3^1/2) = log 2+1/2 log 3 = 0.30103+1/2(0.47712) = 0.30103+0.23856 =0. 53959

19. log₂ 16 = log₂2⁴ = 4 log₂ 2 = 4

23. ln e² = 2ln e = 2

27 log_1/5 25 = log_1/5 5⁵ = log_1/5 (1/5)^-5 = -5 log_1/5(1/5) = -5

31 log (10¹⁰⁰) = 100 log 10 = 100

43. Since log 1000 = log (10³), hence log(10³) = 3

45. ln(x+1) = 2 or x+1 = e² or, x = e² -1.

47. log_x 10 = 3 or 3 log_x x = log_x 10 or, log _x x³ = log_x 10 or, x³ = 10.