91Ó°ÊÓ

write each equation in its equivalent logarithmic form. $$13^{2}=x$$

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$6^{\frac{x-3}{4}}=\sqrt{6}$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible,evaluate logarithmic expressions without using a calculator. $$\log _{b} x^{3}$$

An artifact originally had 16 grams of carbon- 14 present. The decay model \(A=16 e^{-0.000121 t}\) describes the amount of carbon-14 present after \(t\) years. How many grams of carbon- 14 will be present in 5715 years?

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$h(x)=\left(\frac{1}{2}\right)^{x}$$

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$h(x)=\left(\frac{1}{3}\right)^{x}$$

An artifact originally had 16 grams of carbon- 14 present. The decay model \(A=16 e^{-0.000121 t}\) describes the amount of carbon-14 present after \(t\) years. How many grams of carbon-14 will be present in \(11,430\) years?

Solve each exponential equation by expressing each side as a power of the same base and then equating exponents. $$7^{\frac{x-2}{6}}=\sqrt{7}$$

write each equation in its equivalent logarithmic form. $$15^{2}=x$$

Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible,evaluate logarithmic expressions without using a calculator. $$\log _{b} x^{7}$$