0. Functions

Evaluate each expression without a calculator.

a. log₁₀ 1000

Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.

$\(\log\)_317$

Evaluate the given logarithm.

$\(\log\)_77^{0.3}$

Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log. 

$\(\log\)_23789$

2. Express the following logarithms in terms of ln 5 and ln 7.

f. (ln35 + ln(1/7))/(ln25)

Evaluate the given logarithm.

$\(\frac\)32\(\log\)1$

1. Express the following logarithms in terms of ln 2 and ln 3.

b. ln(4/9)

4. Use the properties of logarithms to write the expressions in Exercises 3 and 4 as a single term.

c. 3ln ∛(t² - 1) - ln(t+1)

Explain why or why not. Determine whether the following statements are true and give an explanation or counterexample.

b. ln(x + 1) + ln(x − 1) = ln(x² − 1), for all x.

1. Express the following logarithms in terms of ln 2 and ln 3.

f. ln √(13.5)

Determine whether the following statements are true and give an explanation or counterexample.

$2=10^{{\log }_{10}2}$

4. Use the properties of logarithms to write the expressions in Exercises 3 and 4 as a single term.

a. ln secθ + ln cosθ

3. Use the properties of logarithms to write the expressions in Exercises 3 and 4 as a single term.

b. ln(3x² - 9x) + ln(1/3x)

Express 3ˣ, x^{π}, and x^{sin x} using the base e.

Properties of logarithms Assume logbx = 0.36, logby= 0.56 and logbz = 0.83 . Evaluate the following expressions.

logbx²