Lial - College Algebra 13th Edition

Ch. 4 - Inverse, Exponential, and Logarithmic Functions

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Lial 13th Edition

Ch. 4 - Inverse, Exponential, and Logarithmic Functions

Section 4.5

Problem 25

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. (1/3)^x = -3

Problem 27

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 0.05(1.15)^x = 5

Problem 29

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 3(2)^x-2 + 1 = 100

Problem 31

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 2(1.05)^x + 3 = 10

Problem 33

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 5(1.015)^x-1980 = 8

Problem 35

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. e^2x - 6e^x + 8 = 0

Problem 37

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 2e^2x + e^x = 6

Problem 39

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. 5^2x + 3(5^x) = 28

Problem 41

Solve each equation. Give solutions in exact form. 5 ln x = 10

Problem 43

Solve each equation. Give solutions in exact form. ln 4x = 1.5

Problem 45

Solve each equation. Give solutions in exact form. log(2 - x) = 0.5

Problem 47

Solve each equation. Give solutions in exact form. log₆ (2x + 4) = 2

Problem 49

Solve each equation. Give solutions in exact form. log₄ (x³ + 37) = 3

Problem 51

Solve each equation. Give solutions in exact form. ln x + ln x² = 3

Problem 53

Solve each equation. Give solutions in exact form. log₃ [(x + 5)(x - 3)] = 2

Problem 55

Solve each equation. Give solutions in exact form. log₂ [(2x + 8)(x + 4)] = 5

Problem 56

Solve each equation. Give solutions in exact form. log₅ [(3x + 5)(x + 1)] = 1

Problem 59

Solve each equation. Give solutions in exact form. log(x + 25) = log(x + 10) + log 4

Problem 63

Solve each equation. Give solutions in exact form. ln(7 - x) + ln(1 - x) = ln (25 - x)

Problem 73

Solve each equation. Give solutions in exact form. ln(4x - 2) - ln 4 = -ln(x - 2)

Problem 79

Solve each equation. Give solutions in exact form. ln e^x - 2 ln e = ln e⁴

Problem 81

Solve each equation. Give solutions in exact form. log₂ (log₂ x) = 1

Problem 83

Solve each equation. Give solutions in exact form. log x² = (log x)²

Problem 87

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. p = a + (k/ln x), for x

Problem 88

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. r = p - k ln t, for t

Problem 91

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. $I = \frac{E}{R} (1 - e^{- \frac{R t}{2}}), for t$

Problem 93

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. y = A + B(1 - e^-Cx), for x

Problem 95

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. log A = log B - C log x, for A

Problem 97

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. A = P (1 + r/n)^tn, for t

Problem 102

To solve each problem, refer to the formulas for compound interest. A = P (1 + r/n)^tn and A = Pe^rt Find t, to the nearest hundredth of a year, if $1786 becomes $2063 at 2.6%, with interest compounded monthly.