Exam 20: Exponential and Logarithmic Functions

Solve for $x$ to three significant digits: $3\left(2^{x+1}\right)+5\left(2^{2 x}\right)=8$

Graph the following function from $x=1 / 4$ to $x=4$ : $y=-2.5 \log _{3}(4-x)$

Find $x$ to three significant digits if the common logarithm of $x$ is equal to: (a) 2.4 (b) -0.83 (c) -12.4 (d) 1.32

Write as the sum or difference of two or more logarithms: $\log \frac{9 b}{3}$

How long will it take a population to triple if it is growing exponentially at a rate of $8 \%$ per year?

Express as a single logarithm with a coefficient of $1: 4 \log z+5 \log y-\log w$

Solve for $x: \log _{2} x=-3$

Solve for $x$ to three significant digits: $e^{4 x+1}=5 e^{x-3}$

Determine the half-life of a radioactive substance that decays exponentially at the rate of 9.5% per year.

Solve for $x: \sqrt[2 x]{6}(42-\sqrt[2 x]{6})=216$

Solve for $x$ to three significant digits: $\log _{3} 3=2 \log _{3} 3 x$

Convert to exponential form: $\log _{3} 81=4$

Solve for $x$ to three significant digits: $2 \ln (x+3)=5$

How much money does a company have to invest in an account that pays $6 \%$ per year, compounded annually, to have $\$ 12,000$ after three years?

Solve for $x$ to three significant digits. Check your answers. [HINT: $\log x=\log _{10} x$ ] $\log (x-4)+2=\log (9-x)$

How long will it take for $\$ 15,000$ to grow to $\$ 32,000$ in a fund earning interest at rate $4.75 \%$ per year compounded annually?

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

Convert to logarithmic form: $3.1^{P}=2.4$

Solve for $x$ to three significant digits: $e^{4 x}-4 e^{2 x}+3=0$

The voltage across a particular capacitor grows exponentially from $0 \mathrm{~V}$ to a maximum of $40.0 \mathrm{~V}$ , at a rate of $8 \%$ per second. What is the voltage at 5.00 seconds?