91Ó°ÊÓ

Answer each of the following. How is \(\log _{3} 12\) written in terms of natural logarithms?

If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. $$10^{-4}=0.0001$$

The exercises in this set are grouped according to discipline. They involve exponential or logarithmic models. An initial amount of a radioactive substance \(y_{0}\) is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form \(y=y_{0} e^{k t}\) that models the situation, give the exact value of \(k\) in terms of natural logarithms. \(y_{0}=30 \mathrm{g} ;\) After \(6 \mathrm{hr}, 10 \mathrm{g}\) remain.

Solve each exponential equation. Express irrational solutions as decimals correct to the nearest thousandth. $$5^{x}=13$$

Solve each exponential equation. Express irrational solutions as decimals correct to the nearest thousandth. $$\left(\frac{1}{2}\right)^{x}=5$$

The exercises in this set are grouped according to discipline. They involve exponential or logarithmic models. An initial amount of a radioactive substance \(y_{0}\) is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form \(y=y_{0} e^{k t}\) that models the situation, give the exact value of \(k\) in terms of natural logarithms. \(y_{0}=10 \mathrm{mg} ;\) The half-life is 100 days.

If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. $$\log _{6} 36=2$$

Answer each of the following. Why is \(\log _{2} 0\) undefined?

If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. $$\log _{5} 5=1$$

Answer each of the following. Between what two consecutive integers must \(\log _{2} 12\) lie?