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Magazine Problem 18
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?
Problem 19
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. $$ \ln \sqrt[5]{x} $$
Problem 19
Use the exponential decay model for carbon- \(14, A-A_{1} e^{-0,0001211}\) to solve Exercises \(19-20 .\) Prehistoric cave paintings were discovered in a cave in France. The paint contained \(15 \%\) of the original carbon- 14 . Estimate the age of the paintings.
Problem 19
Write each equation in its equivalent logarithmic form. $$ 7^{y}=200 $$
Problem 20
Write each equation in its equivalent logarithmic form. $$ 8^{y}=300 $$
Problem 20
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. $$ \ln \sqrt[7]{x} $$
Problem 20
Use the exponential decay model for carbon- \(14, A-A_{1} e^{-0,0001211}\) to solve Exercises \(19-20 .\) 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?
Problem 21
Evaluate each expression without using a calculator. $$ \log _{4} 16 $$
Problem 21
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. $$ \log _{b}\left(x^{2} y\right) $$
Problem 22
Evaluate each expression without using a calculator. $$ \log _{7} 49 $$
