1). Without using a graph utility, sketch the graph of f(x) =3^x-5
2) A certain population grows according to the equation Y=40e^0.025t. Find the initial population (to the nearest integer) when t=50.
3) Write in exponential from: logb 37=2.
4) Write as sum, difference, or multiple of logarithms: in 5x/3â??X^2+1
5) Write as the logarithm of single quantity: 1/5[3 log(x+1)+2 log(x-1)-log7].
6) Solve x: 2x+in e^4x=12.
7) Solve x: log3(x^2+5)=log3(4x^2-2x).
8) Determine the annual rate of interest compounded continuously for the sum of money in an account to become triple the original amount in 10 years.
9) The spread of flu virus through a certain population is modeled by:
Y=1000/1+990e^-0.7t. Where y is the total number infected after t days. In how many days will 612 people be infected with the virus?
10) Evaluate logA 9/2, given logA 2=0.2789, logA 3=0.4421.
11) Find the equation of the inverse of f(x)=5x+2. Graph f and f^-1 on the same set of axes.
12) Show that if f(x) = 4x-1, then f^-1(x) = x+1/4
This solution uses the properties of logarithms to simplify the logarithm expression into a single log.