Exponential and Logarithmic Functions

Evaluating the natural Exponential Function

100

Evaluate the function given by f(x) = e^x when x=-2

f(-2) = e^-2 = 0.13533553

200

h(x) = e^-x x=3/4

0.472

300

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

7166.647

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

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

Logarithmic Functions

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 5

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

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.

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

500

ln((x^2)-2) = ln23 USe the inverse property to solve for x.

x=-5,5

Properties of Logarithms

100

Evaluate  log(subscript 4)25

log25/log4 2.3219

200

Evaluate log(subscript 2) 12.

ln12/ln2 =3.5850

300

Use the properties of logarithms to expand 

=ln2 - ln27 =ln2 - ln3^3 =ln2-3ln3

400

Condense the expression to the logarithm of a single quantity. 1/4log(subscript 3) 5x

log (subscript 3) 5x to the fourth root

500

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

logx/logy^2 + logz^3 =logx/logy^2 x logz^3 =logxz^3/y^2

Exponential and Logarithmic Equations

100

Solve. e^x=7

lne^x=ln7 x=ln7

200

e^x +5=60 Solve.

e^x=55 lne^x=ln55 x=ln55=4.007

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

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

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