91Ó°ÊÓ

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

An artifact originally had 16 grams of carbon- 14 present. The decay model \(A=16 e^{-0.0001211}\) describes the amount of carbonI 4 present, \(A,\) in grams, after \(t\) years. The half-life of the radioactive element plutonium-239 is \(25,000\) years. If 16 grams of plutonium- 239 are initially present how many grams are present after \(25,000\) years? \(50,000\) years? \(75,000\) years? \(100,000\) years? \(125,000\) years?

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. \(f(x)=(0.6)^{x}\)

Solve each exponential equation in Exercises \(1-26\) Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$7^{0.3 x}=813$$

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. $$ \log N^{-6} $$

Write each equation in its equivalent logarithmic form. $$b^{3}=1000$$

Write each equation in its equivalent logarithmic form. $$b^{3}=343$$

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. $$ \log M^{-8} $$

Use the exponential decay model for carbon- 14 \(A=A_{0} e^{-0.000121 t},\) Skeletons were found at a construction site in San Francisco in \(1989 .\) The skeletons contained \(88 \%\) of the expected amount of carbon-14 found in a living person. In \(1989,\) how old were the skeletons?

Solve each exponential equation in Exercises \(1-26\) Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. $$3^{x / 7}=0.2$$