Exam 20: Exponential and Logarithmic Functions

Write as the sum or difference of two or more logarithms: $\log \frac{2 a b}{c}$

A room initially $20.0^{\circ} \mathrm{C}$ above the outside temperature cools exponentially at a rate of $20 \%$ per hour. Find the temperature of the room (above the outside temperature) after $150 \mathrm{~min}$ .

Solve for $x$ : $\left(9^{x+1}\right)^{x-2}=1$

A quantity grows exponentially from 0 to a maximum of 100 at a rate of $8 \%$ per second. Write the equation for the quantity at any second. What is the quantity at $5.0 \mathrm{~s}$ ?

Solve for $x$ : $\log x^{3}=\frac{2+\log x}{2-\log x}$

Find $x$ to three significant digits if the common logarithm of $x$ is equal to: (a) -2.087 (b) 5.917 (c) -1.015 (d) 3.617

Solve for $x: 3^{2+\log x}-3^{1+\log x}+3^{\log x}=21$

Solve for $x$ to three significant digits. Check your answers. [HINT: $\log x=\log _{10} x$ ] $\log (2 x-3)-\log (3 x+2)=\log (4 x-7)-\log (6 x-5)$

Solve for $x$ to three significant digits: $4\left(5^{2 x-3}\right)=75$

Solve for x: $\log_x 81 = 4$

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

A student invests $\$ 4,000$ in an account that pays $5 \%$ interest per year, compounded annually. How much interest does the student earn if he leaves the money in the account for three years?

$\operatorname{Graph} {y=2.8 e^{0.2 x}}$ on semilog paper.

Graph $y=1.25^{2 x}$ on semilog paper.

Convert to exponential form: $\log _{a} c=b$

Express as a single logarithm with a coefficient of $1: 4 \log x-3 \log y-2 \log z$

Rewrite the equation so that it contains no logarithms: $2 \log _{3} x-\log _{3}\left(x^{2}-1\right)=1$

If an amount of money $P$ is deposited annually for $t$ years into an account with an interest rate $r$ ,it will accumulate to a value $V$ according to the equation $V=P\left(\frac{(1+r)^{t}-1}{r}\right)$ . If someone pays $\$ 5000$ annually, what will the value of the account be after 20 years?

Convert to logarithmic form: $10^{x}=5 y$

Solve for $x$ to three significant digits: $9^{\sqrt{x+2}}=27$