6. Exponential & Logarithmic Functions

Properties of Logarithms

Open Question
In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement.log6 [(x - 1)/(x^2 + 4)] = log6 (x - 1) - log6 (x^2 + 4)
Multiple Choice
Write the log expression as a single log.
$\log_2\frac{1}{9x}+2\log_23x$
Multiple Choice
Write the log expression as a single log.
$\ln\frac{3x}{y}+2\ln2y-\ln4x$
Multiple Choice
Write the single logarithm as a sum or difference of logs.
$\log_3\left(\frac{\sqrt{x}}{9y^2}\right)$
Multiple Choice
Write the single logarithm as a sum or difference of logs.
$\log_5\left(\frac{5\left(2x+3\right)^2}{x^3}\right)$
Multiple Choice
Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.
$\log_317$
Multiple Choice
Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.
$\log_967$
Multiple Choice
Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.
$\log_841$
Multiple Choice
Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.
$\log_23789$
Open Question
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.log5 (7 × 3)
Open Question
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.log7 (7x)
Open Question
In Exercises 1–8, write each equation in its equivalent exponential form. 5= logb 32
Open Question
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.log(1000x)
Open Question
Answer each of the following. Write log_3 12 in terms of natural logarithms using the change-of-base theorem.
Open Question
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.log7 (7/x)