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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) = log(subscript 2)x x=32

f(32) = log(subscript 2)32 = 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

 x=ln7

x= 1.9459

200
What is the x-intercept of all non translated exponential graphs
(0,1)
200
h(x) = e^-x 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 

200
use the natural logarithms changing base formula to solve log(subscript 2) 12.
ln12/ln2 =3.5850
200

e^x +5=60 Solve.

x=ln55

x=4.007

300

Use the graph of f to describe the transformation that yields the graph of the function. f(x)= (7/2)^x, g(x)= -(7/2)^(x-6)

Reflect the graph of f in the x-axis and shift six units to the right.

300
f(x) = 5000e^0.06x x=6
7166.647
300

Evaluate the function f(x) = logx when 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.

t=3.417

400

True or False, the line y=-2 is an asymptote for the graph of f(x) = 10^x-2. Justify your answer.

true because it will go left until for negative infinity, but it will get so close to -2 but never touch, making -2 an asymptote.

400

A total of 12000 is invested at an annual interest rate 9%. Find the balance after 5 years if it is compounded continuously. Use the formula A=Pe^(rt)

=12,000e^(0.09(5)) =18,819.75

400

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

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.

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 quarterly.

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 

Solve for x.

x=-5,5

500

logx - 2logy + 3logz. condense to a single quantity.

logx/logy^2 + logz^3 =(logx/logy^2)( logz^3) =log((xz^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