91Ó°ÊÓ

Find the inverse of each one-to-one function. $$ f(x)=(x-5)^{3} $$

Solve each equation for \(x\). Give an exact solution and a four-decimal-place approximation. See Examples 3 and 7. $$ \ln x=2.1 $$

Find the value of each logarithmic expression. See Examples 3 and 5. $$ \log _{10} \frac{1}{10} $$

The size of the wolf population at Isle Royale National Park increases at a rate of \(4.3 \%\) per year. If the size of the current population is 83 wolves, find how many there should be in 5 years. Use \(y=y_{0} e^{0.043 t}\) and round to the nearest whole.

Solve each equation for \(y\). $$ x=-2 y-7 $$

Write each expression as a sum or difference of logarithms. Assume that variables represent positive numbers. See Example 5. $$ \log _{4} \frac{2}{9 z} $$

Solve each equation for \(x\). Give an exact solution and a four-decimal-place approximation. See Examples 3 and 7. $$ \ln (3 x-4)=2.3 $$

Solve each equation for \(y\). $$ x=4 y+7 $$

Solve. Unless otherwise indicated, round results to one decimal place. See Example 6. An accidental spill of 75 grams of radioactive material in a local stream has led to the presence of radioactive debris decaying at a rate of \(4 \%\) each day. Find how much debris still remains after 14 days, Use \(y=75(2.7)^{-0.04 t}\)

Solve each equation for \(x\). Give an exact solution and a four-decimal-place approximation. See Examples 3 and 7. $$ \ln (2 x+5)=3.4 $$