Graphing
Evaluating the natural Exponential Function
Logarithmic Functions
Properties of Logarithms
Exponential and Logarithmic Equations
100
What would be the transformation of 3^x+1
It translated one unit up
100
Evaluate the function given by f(x) = e^x when x=-2
f(-2) = e^-2 = 0.13533553
100

Use the definition of logarithmic function to evaluate each logarithmic at the indicated value of x. f(x) = log2x at x=32

f(32) = log232 = 5 because 2^5=32 

100
Use the changing base formula to solve log(subscript 4)25
log25/log4 2.3219
100
Solve. e^x=7
lne^x=ln7 x=ln7
200

What is the x-intercept of the parent function f(x) = 2x

(0,1)

200

h(x) = e-x at x=3/4

0.472

200

Use the definition of logarithmic function to evaluate each logarithmic at the indicated value of x. f(x) = logx, x=1/100.

f(1/100)= log1/100=-2 -2

200
use the natural logarithms changing base formula to solve log(subscript 2) 12.
ln12/ln2 =3.5850
200
e^x +5=60 Solve.
e^x=55 lne^x=ln55 x=ln55=4.007
300

Find the Domain, x-intercept, and vertical asymptote of the logarithmic function and describe the graph. g(x) = ln(-x)

Domain: (-infinity, 0) x-intercept: (-1,0) Vertical asymptote: x=0 The Graph will come the upper left quadrant and pass through (-1,0) and then travel close the x=0 till infinity without touching it.

300
f(x) = 5000e^0.06x x=6
7166.647
300
evaluate for the function f(x) = logx x=-2
No solution, no real number power to which 10 can be raised to obtain -2.
300
Use the properties of logarithms to write the logarithms in terms of ln2 and ln3 : ln2/27
=ln2 - ln27 =ln2 - ln3^3 =ln2-3ln3
300
2(3^2t-5)-4=11 Solve.
2(3^2t-5)=15 3^2t-5=15/2 log(subscript 3)3^2t-5=log (subscript 3) 15/2 2t-5=log(subscript 3)7.5 t=5/2 +1/2log(subscript 3)7.5 t=3.417
400

True or False, the line y=-2 is an asymptote for the graph of f(x) = 10x - 2. Justify your answer. No graphing utilities are permitted for this question.

true because as x approaches negative infinity, f(x) approaches -2 but never touches it.

400
A total of 12000 is invested at an annual interest rate 9%. Find the balance after 5 years if it is compounded. Use the formula A=Pe^rt
=12,000e^0.09(5) =18,819.75
400
Use the one to one property to solve log(x^2 - 6) = log10.
x^2 -6 = 10 x^2 = 16 x= plus or minus 4
400
Condense the expression to the logarithm of a single quantity. 1/4log(subscript 3) 5x
log (subscript 3) 5x to the fourth root
400
Solve. 5+2lnx=4
5+2lnx=4 2lnx=-1 lnx=-1/2 e^lnx=e^-1/2 x=e^-1/2 x=0.607
500

What is the equation of the asymptote of the function f(x) = ln(x - 1) + 4?

x = 1

500
With the given formula for compounding per year: A=P(1+r/n)^nt. A total of 12000 is invested at an annual interest rate 9%. Find the balance after 5 years if it is compounded. Find the quarterly compounding by setting n=4.
A=P(1+r/n)^nt = 12000(1+ 0.09/4)^4(5) approximately equal to 18,726.11
500
ln((x^2)-2) = ln23 USe the One to One property to solve for x.
x=-5,5
500
logx - 2logy + 3logz. condense to a single quantity.
logx/logy^2 + logz^3 =logx/logy^2 x logz^3 =logxz^3/y^2
500
You have deposited $500 in account that pays 6.75% interest, compounded continuously. how long will it take to double? Use the formula A=Pe^rt
A=500e^0.0675t=1000 e^0.0675t=2 lne^0.0675t=ln2 0.0675t=ln2 t=ln2/0.0675 t=10.27
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