Chapter 4

Fill in the blank: The logarithm of a product of two numbers is equal to the _____ of their logarithms.

Fill in the blank. The inverse of an exponential function is a(n) ____________ function.

Fill in the blank. Functions that involve some combination of basic arithmetic operations, powers, or roots are ______ functions

Fill in the blank. A base 10 logarithm is a(n) __________ logarithm.

Fill in the blank: The logarithm of a power of a number is equal to the _____ times the logarithm of the number.

Fill in the blank. Base \(e\) logarithm is a(n) _____________ logarithm.

Fill in the blank. A function of the form \(f(x)=a^{x}\) where \(a\) and \(x\) are real numbers with \(a>0\) and \(a \neq 1\) is a(n) _____ function.

Fill in the blank. The domain of \(f(x)=a^{x}\) for \(a>0\) is the set of _________.

Simplify each expression. $$e^{\ln (\sqrt{y})}$$

Fill in the blank. The \(y\) -axis is a(n) _____________ for the graph of \(f(x)=\log _{a}(x)\).

Fill in the blank. The function \(f(x)=a^{x}\) is ________ if \(a>1\) and ______ if \(0

Simplify each expression. $$10^{\log (3 x+1)}$$

Fill in the blank. The ______________ of the function \(f(x)=\log _{a}(x)\) is \((0, \infty)\).

Fill in the blank. The graph of \(f(x)=a^{x}\) has the \(x\) -axis as a(n) _________.

Simplify each expression. $$\log \left(10^{y+1}\right)$$

Simplify each expression. $$\ln \left(e^{2 x}\right)$$

Fill in the blank. The _____________ property of logarithms indicates that if \(\log _{a}(m)=\log _{a}(n),\) then \(m=n\).

Simplify each expression. $$7^{\log _{7}(999)}$$

Determine the number that can be used in place of the question mark to make the equation true. $$2^{?}=64$$

Evaluate each exponential expression without using a calculator. $$3^{3}$$

Simplify each expression. $$\log _{4}\left(2^{300}\right)$$

Determine the number that can be used in place of the question mark to make the equation true. $$2^{?}=16$$

Evaluate each exponential expression without using a calculator. $$2^{5}$$

Rewrite each expression as a single logarithm. $$\log (5)+\log (3)$$

Determine the number that can be used in place of the question mark to make the equation true. $$3^{?}=\frac{1}{81}$$

Evaluate each exponential expression without using a calculator. $$-2^{0}$$

Rewrite each expression as a single logarithm. $$\ln (6)+\ln (2)$$

Determine the number that can be used in place of the question mark to make the equation true. $$3^{?}=1$$

Evaluate each exponential expression without using a calculator. $$-4^{0}$$

Rewrite each expression as a single logarithm. $$\log _{2}(x-1)+\log _{2}(x)$$

Determine the number that can be used in place of the question mark to make the equation true. $$16^{?}=2$$

Evaluate each exponential expression without using a calculator. $$2^{-3}$$

Rewrite each expression as a single logarithm. $$\log _{3}(x+2)+\log _{3}(x-1)$$

Determine the number that can be used in place of the question mark to make the equation true. $$16^{?}=16$$

Evaluate each exponential expression without using a calculator. $$3^{-2}$$

Each of these equations involves more than one logarithm. Solve each equation. Give exact solutions. $$\log _{2}(x+2)+\log _{2}(x-2)=5$$

Rewrite each expression as a single logarithm. $$\log _{4}(12)-\log _{4}(2)$$

Evaluate each exponential expression without using a calculator. $$\left(\frac{1}{2}\right)^{-4}$$

Each of these equations involves more than one logarithm. Solve each equation. Give exact solutions. $$\log _{6}(w-1)+\log _{6}(w-2)=1$$

Rewrite each expression as a single logarithm. $$\log _{2}(25)-\log _{2}(5)$$

Determine the number that can be used in place of the question mark to make the equation true. $$\left(\frac{1}{5}\right)^{?}=\frac{1}{125}$$

Evaluate each exponential expression without using a calculator. $$\left(\frac{1}{3}\right)^{-2}$$

Each of these equations involves more than one logarithm. Solve each equation. Give exact solutions. $$\log \left(\frac{x-3}{2}\right)+\log \left(\frac{x+2}{7}\right)=0$$

Rewrite each expression as a single logarithm. $$\ln \left(x^{8}\right)-\ln \left(x^{3}\right)$$

Find the indicated value of the logarithmic functions. $$\log _{2}(64)$$

Evaluate each exponential expression without using a calculator. $$8^{2 / 3}$$

Each of these equations involves more than one logarithm. Solve each equation. Give exact solutions. $$\log _{2}\left(\frac{a-2}{5}\right)+\log _{2}\left(\frac{a+3}{10}\right)=0$$

Rewrite each expression as a single logarithm. $$\log \left(x^{2}-4\right)-\log (x-2)$$

Find the indicated value of the logarithmic functions. $$\log _{2}(16)$$

Evaluate each exponential expression without using a calculator. $$9^{3 / 2}$$