1.5 Exponential and logarithmic functions  (Page 8/17)

$f\left(x\right)=e^x+2$

$f\left(x\right)=\text{−}{2}^x$

$f\left(x\right)=3^{x+1}$

$f\left(x\right)=4^x-1$

$f\left(x\right)=1-2^{\text{−}x}$

$f\left(x\right)=5^{x+1}+2$

$f\left(x\right)=e^{\text{−}x}-1$

${\text{log}}_{3}81=4$

${\text{log}}_{8}2=\frac{1}{3}$

${\text{log}}_{5}1=0$

${\text{log}}_{5}25=2$

$\text{log}0.1=\mathrm{-1}$

$\text{ln}\left(\frac{1}{e^3}\right)=\mathrm{-3}$

${\text{log}}_{9}3=0.5$

$\text{ln}1=0$

$2^3=8$

$4^{\mathrm{-2}}=\frac{1}{16}$

${10}^2=100$

$9^0=1$

${\left(\frac{1}{3}\right)}^3=\frac{1}{27}$

$\sqrt[3]{64}=4$

$e^x=y$

$9^y=150$

$b^3=45$

$4^{\mathrm{-3}\text{/}2}=0.125$

$f\left(x\right)=3+\text{ln}x$

$f\left(x\right)=\text{ln}(x-1)$

$f\left(x\right)=\text{ln}(\text{−}x)$

$f\left(x\right)=1-\text{ln}x$

$f\left(x\right)=\text{log}x-1$

$f\left(x\right)=\text{ln}(x+1)$

$\text{log}{x}^{4}y$

${\text{log}}_3\frac{9a^3}{b}$

$\text{ln}a\sqrt[3]{b}$

${\text{log}}_5\sqrt{125x{y}^3}$

${\text{log}}_4\frac{\sqrt[3]{xy}}{64}$

$\text{ln}\left(\frac{6}{\sqrt{e^3}}\right)$

$5^x=125$

$e^{3x}-15=0$

$8^x=4$

$4^{x+1}-32=0$

$3^{x\text{/}14}=\frac{1}{10}$

${10}^x=7.21$

$4·2^{3x}-20=0$

$7^{3x-2}=11$

${\text{log}}_{3}x=0$

${\text{log}}_{5}x=\mathrm{-2}$

${\text{log}}_4\left(x+5\right)=0$

$\text{log}\left(2x-7\right)=0$

$\text{ln}\sqrt{x+3}=2$

${\text{log}}_6\left(x+9\right)+{\text{log}}_{6}x=2$

${\text{log}}_4\left(x+2\right)-{\text{log}}_4\left(x-1\right)=0$

$\text{ln}x+\text{ln}\left(x-2\right)=\text{ln}4$

${\text{log}}_{5}47$

${\text{log}}_{7}82$

${\text{log}}_{6}103$

${\text{log}}_{0.5}211$

${\text{log}}_2\pi$

${\text{log}}_{0.2}0.452$

Rewrite the following expressions in terms of exponentials and simplify.

a. $2\text{cosh}\left(\text{ln}x\right)$ b. $\text{cosh}4x+\text{sinh}4x$ c. $\text{cosh}2x-\text{sinh}2x$ d. $\text{ln}\left(\text{cosh}x+\text{sinh}x\right)+\text{ln}\left(\text{cosh}x-\text{sinh}x\right)$

[T] The number of bacteria N in a culture after t days can be modeled by the function $N\left(t\right)=1300·{\left(2\right)}^{t\text{/}4}.$ Find the number of bacteria present after 15 days.

[T] The demand D (in millions of barrels) for oil in an oil-rich country is given by the function $D\left(p\right)=150·{\left(2.7\right)}^{\mathrm{-0.25}p},$ where p is the price (in dollars) of a barrel of oil. Find the amount of oil demanded (to the nearest million barrels) when the price is between $15 and $20.

[T] The amount A of a $100,000 investment paying continuously and compounded for t years is given by $A\left(t\right)=\mathrm{100,000}·e^{0.055t}.$ Find the amount A accumulated in 5 years.

[T] An investment is compounded monthly, quarterly, or yearly and is given by the function $A=P{\left(1+\frac{j}{n}\right)}^{nt},$ where $A$ is the value of the investment at time $t,P$ is the initial principle that was invested, $j$ is the annual interest rate, and $n$ is the number of time the interest is compounded per year. Given a yearly interest rate of 3.5% and an initial principle of $100,000, find the amount $A$ accumulated in 5 years for interest that is compounded a. daily, b., monthly, c. quarterly, and d. yearly.