Logarithms

Logarithm Expressions

3. For what value of x is the equation 22′ 7 = 215 true?

2017 April(74F) Math Question 3

2019 June(72F) Math Question 14

26. What is the value of the expression _log6(36)+_log3(9)+ ?

2021 June(D06) Math Question 26

2018 April(A09) Math Question 33

2017 June(74C) Math Question 35

2019 December(C03) Math Question 36

2020 June(C02) Math Question 41

2019 April(B04) Math Question 42

2020 July(C01) Math Question 42

42. The number of decibels, d, produced by an audio source can be modeled by the equation d = 10 log(7), where I is the sound intensity of the audio source and K is a constant. How many decibels are produced by an audio source whose sound intensity is 1,000 times the value of K ?

2017 April(74F) Math Question 42

45. The value of log(x), to the nearest 0.1, is given in the table below for 4 different values of x. To the nearest 0.1, what is the value of log(3 × 105,000) ?

Laws of Logarithms

2021 April(D05) Math Question 45

47. For all x > 0, which of the following expressions is equivalent to log ((2x)-) ?

2013 June(71C) Math Question 47

48. For positive real numbers M and N, log M/N = ?

2021 April(D05) Math Question 48

2009 April(66F) Math Question 49

51. What value of x satisfies the equation below?

2014 December(72G) Math Question 51

2011 April(67F) Math Question 52

53. Which of the following values is the x-coordinate of the point in the standard (x,y) coordinate plane where the graph of the line y = 7 intersects the graph of the function y = ln(x — 2) + 3 ?

2017 June(74C) Math Question 53

Laws of exponents

2020 December(D03) Math Question 53

54. Which of the following number line graphs represents all values in the domain of the function y = loglo(x2 — 4x + 3) ?

2016 December(74H) Math Question 54

54. For positive integers x and  y where x < 8, logx,8 = y. What is the value of y ?

2021 December(E23) Math Question 54

60. For what real value of x, if any, is log(x+3)(x^2+ 3) = 2

Logarithm ExpressionsLogarithmsACT math questions

2017 April(74F) Math Question 3

2019 June(72F) Math Question 14