Exam 20: Exponential and Logarithmic Functions

Find the natural logarithm of each number to four decimal places: (a) 53.1 (b) 8080 (c) 0.00381 (d) 2.01

Solve for $x$ : ${10^{8 x}-9}\left(10^{4 x}\right)+18=0$

Solve for $x$ : $8 e^{3 x-1}=75$

A culture of bacteria has a population that doubles every hour. Find the population of the bacteria after 4 hours if the initial population is 750 .

A bacteria grows exponentially at a rate of $25.0 \%$ per hour for 5 hours. Find the final amount if the initial amount is 1000 .

Solve for $x: \log _{a} x-\log _{a^{2}} x+\log _{a^{3}} x=5$

Graph $y=2 x^{0.5}$ on log-log paper for $x=1$ to 10 .

Find the natural logarithm of each number to four decimal places: (a) 27 (b) 6.55 (c) 0.14 (d) 672

Convert to logarithmic form: $3^{X}=9$

Graph $y=1.2^{x}$ on semilog paper.

Solve for $x$ to three significant digits: $(9.90)^{x-3}=11.0$

Convert to logarithmic form: $h^{2 / 3}=8.8$

Solve for $x$ : $4 e^{2 x+1}=5 e^{x-3}$

Express as a single logarithm with a coefficient of 1 : $\frac{\log z}{2}+5 \log x-2 \log y$

Convert to exponential form: $\log _{0.5} 16=-4$

The value of a mortgage $M$ can be found using $M=P\left(\frac{1-\left(1+\frac{r}{12}\right)^{-12 t}}{\frac{r}{12}}\right)$ , where $P$ is the monthly payment, $r$ is the interest rate compounded monthly and $t$ is the number of years for the mortgage. What would the monthly payment be for a $\$ 250,000$ mortgage with a $6 \%$ interest compounded monthly for 20 years?

Solve for $x: 125^{\frac{2 x}{3}+1}+125^{\frac{x+1}{3}}=6$

If an investment will double its value in 4 years, what annual compound interest rate (compounded annually) is being earned?

Simplify: $\log _{5} 5^{y}$

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