91Ó°ÊÓ

Find the domain of each logarithmic function. $$f(x)=\ln (x-2)^{2}$$

In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ 4 \ln (x+6)-3 \ln x $$

What is the natural exponential function?

Use a calculator to evaluate \(\left(1+\frac{1}{x}\right)^{x}\) for \(x=10,100\) \(1000,10,000,100,000,\) and \(1,000,000 .\) Describe what happens to the expression as \(x\) increases.

Find the domain of each logarithmic function. $$f(x)=\ln (x-7)^{2}$$

In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ 8 \ln (x+9)-4 \ln x $$

Evaluate each expression without using a calculator. $$\log 100$$

In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ 3 \ln x+5 \ln y-6 \ln z $$

In Exercises \(41-70\), use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is \(I .\) Where possible, evaluate logarithmic expressions. $$ 4 \ln x+7 \ln y-3 \ln z $$

Evaluate each expression without using a calculator. $$\log 1000$$