# Math Questions With Answers (3) Logarithms and Exponentials

A set of math questions related to exponential and logarithmic expressions and equations are presented. The answers are provided and are located at the lower part of the page.

 Questions 1: Evaluate the given exponential expressions without using a calculator. A. 1040.5 B. 10log(9) / 2 C. e3 ln(4) D. 10-2 Log(4) E. e2 Ln(4) - ln(16) Questions 2: Evaluate the following logarithmic expressions without using a calculator. A. Log9(3) B. Log2(1/8) C. Log2(400) - Log2(100) D. Log8(4) E. Log5(600) - Log5(24) Questions 3: Solve the following exponential equations. A. ex = 4 B. ex = π 2 C. 4log4(3x - 2) = 10 D. 10log10(3x) = 15 E. 3x+1 + 3x + 3x-1 = 39 Questions 4: Solve the following logarithmic equations. A. ln(ln(x)) = 4 B. ln(x) - ln(4) = 2 ln(x) - ln(16) C. (ln(x))5 = 255/2 D. Log(x - 1) = Log(6) - Log(x) E. Log3(3x+1 - 18) = 2 F. Log7(x) + Logx(7) = 2 G. Logx(27) = 3/4 ANSWERS TO ABOVE QUESTIONS Answers to Questions 1: A. 1040.5 = 104 * 0.5 = 102 = 100 B. 10log(9) / 2 = 10log(91/2) = 3 C. e3 ln(4) = e ln(43) = 43 = 64 D. 10-2 Log(4) = 10Log(4-2) = 4-2 = 1/16 E. e2 Ln(4) - ln(16) = eLn(42) - ln(16) = e0 = 1 Answers to Questions 2: A. Log9(3) = Log9(91/2) = 1/2 B. Log2(1/8) = Log2(2-3) = -3 C. Log2(400) - Log2(100) = Log2(400/100) = 2 D. Log8(4) = Log8(82/3) = 2/3 E. Log5(600) - Log5(24) = Log5(600/24) = Log5(25) = 2 Answers to Questions 3: A. x = ln(4) B. x = 2 ln(π) C. 3x - 2 = 10 , x = 4 D. 3x = 15 , x = 5 E. Multiply all terms of the equation by 3 to obtain 3x+2 + 3x+1 + 3x = 39 *3 Factor 3x out: 3x(9 + 3 + 1) = 39 * 3 Simplify : 3x = 9 and solve: x = 2 Answers to Questions 4: A. Solve for ln(x): ln(x) = e4 , solve for x: x = ee4 B. rewrite equation: ln(x/4) = ln(x2/16) , gives: x/4 = x2/16 , solve for x: x = 4 C. rewrite equation: (ln(x))5 = 55 , gives: ln(x) = 5 , solve for x: x = e5 D. Rewrite as: Log(x - 1) = Log(6/x) , gives: x - 1 = 6/x, solve for x and check: x = 3 is the only solution. E. Rewrite without Log: 3x+1 - 18 = 32, solve for x: x = 2 F. Use change of base formula to rewrite equation: ln(7) / ln(x) + ln(x) / ln(7) = 2 rewrite as: (ln(7))2 + (ln(x))2 - 2ln(7) ln(x) = 0 ( ln(7) - ln(x) )2 = 0 , which gives: ln(7) = ln(x) solve for x: x = 7 G. Rewrite without Log: x3/4 = 27 , solve for x: x = 34 More math questions and problems with detailed solutions in this site.