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Magazine Problem 4
Simplify using logarithm properties to a single logarithm. $$ -\log _{4}\left(\frac{1}{5}\right) $$
Problem 4
The half-life of Fermium- 253 is 3 days. If a sample contains \(100 \mathrm{mg}\), how many milligrams will remain after 1 week?
Problem 4
For each table below, could the table represent a function that is linear, exponential, or neither? $$ \begin{array}{|c|l|l|l|l|} \hline \mathbf{x} & 1 & 2 & 3 & 4 \\ \hline \mathbf{h}(\mathbf{x}) & 70 & 49 & 34.3 & 24.01 \\ \hline \end{array} $$
Problem 4
Rewrite each equation in exponential form. $$ \log _{p}(z)=u $$
Problem 5
For each table below, could the table represent a function that is linear, exponential, or neither? $$ \begin{array}{|c|l|l|l|l|} \hline \mathbf{x} & 1 & 2 & 3 & 4 \\ \hline \mathbf{m}(\mathbf{x}) & 80 & 61 & 42.9 & 25.61 \\ \hline \end{array} $$
Problem 5
Simplify using logarithm properties to a single logarithm. $$ \log _{3}\left(\frac{1}{10}\right)+\log _{3}(50) $$
Problem 5
For each function, find the domain and the vertical asymptote $$ f(x)=\log (3 x+1) $$
Problem 5
The half-life of Erbium- 165 is 10.4 hours. After 24 hours a sample has been reduced to a mass of \(2 \mathrm{mg}\). What was the initial mass of the sample, and how much will remain after 3 days?
Problem 6
The half-life of Nobelium-259 is 58 minutes. After 3 hours a sample has been reduced to a mass of \(10 \mathrm{mg}\). What was the initial mass of the sample, and how much will remain after 8 hours?
Problem 6
For each function, find the domain and the vertical asymptote $$ f(x)=\log (2 x+5) $$
