Exam 20: Exponential and Logarithmic Functions

If an investment grows $75 \%$ in 4 years, what annual compound interest rate (compounded annually) is being earned?

Solve for $x: \log^{2} x=2+\log x$

Convert to logarithmic form: $4^{x / 2}=25$

Solve for $x: \log _{16} 2=x$

The half-life of phosphorus-32 is 14.29 days and decays according to the formula $F=A e^{-0.0485 t}$ , where $F$ is the final amount, $A$ is the initial amount and $t$ is the time in days. How much phosphorus- 32 is left after 60 days, if the initial amount was $25.0 \mathrm{mg}$ ?

Solve for $x$ to three significant digits: $4(10)^{x-1}-3(10)^{x-2}=1$

Solve for $x: \log _{x-2}\left(x^{3}-56\right)=3$

Rewrite the equation so that it contains no logarithms: $3 \log x+\log (x-2)=1+\log (x+3)$

Solve for $x$ to three significant digits: $2 \log x=1+\log (x+1)$

How long will it take the population of a city to halve if it is decreasing exponentially at a rate of $11 \%$ per year?

The $\mathrm{pH}$ value of a solution having a concentration $C$ of hydrogen ions is $\mathrm{pH}=-\log C$ . Find the hydrogen ion concentration of a solution having a $\mathrm{pH}$ of 4.5 .

Find $x$ to three significant digits if the natural logarithm of $x$ is equal to: (a) 1.5 (b) 0.091 (c) -2.37 (d) -0.64

Express as a single logarithm with a coefficient of 1 : $3 \log \frac{a}{p}+\log \frac{b}{q}-\log \frac{c}{r}$

Convert to exponential form: $\log _{3} 24=y$

Solve for $x: \frac{1}{4-2 \log x}-\frac{2}{2+\log x}=1$

Graph $y=5 \sqrt[4]{x}$ on log-log paper for $x=1$ to 10 .

Solve for $x$ to three significant digits: $4^{-2 x}=2(4)^{-3 x}$

Convert to exponential form: $\log _{2.5}(x-3)=-5.5$

Convert to logarithmic form: $6^{5}=7,776$

Solve for $x$ to three significant digits: $3\left(2^{1-x}\right)+7\left(2^{2-x}\right)+2^{3-x}=8$