Chapter 3 - Exponential and Logarithmic Functions

3.1 - Exponential Functions

100

4^x+1 = 256

x = ?

x = 3

200

(1/3)^x = 243

x = ?

x = -5

300

e^{x^2 - 24} = e^2x

x = ?

x = 6

x = -4

400

f(x) = 8000e^0.04x

x = 2

f(x) = ?

f(x) = 8666.297

500

On the day of Logan's birth, Todd deposits $25,000 in a trust fund that pays 6% interest, compounded continuously. Determine the balance in this account on Logan's 27th birthday. Round to two decimal places.

$126,327.26

3.2 - Logarithmic Functions

100

log₆(36) = x

x = ?

x = 2

200

5² = 25

Write the following exponential equation in the form of a logarithmic equation

log₅(25) = 2

300

log_129468349(1) = x

x = ?

x = 0

400

Simplify the following expression

log(25) + log(5) = ?

 = log(125)

500

Write the following expression in logarithmic form

e⁵ = 148.4131

ln(148.4131) = 5

3.3 - Properties of Logs

100

Change the following logarithm to be in the form of common logs

log₈(91)

log(91) / log(8)

200

Use the properties of logarithms to write the logarithm in terms of log₇(3) and log₇(5)

log₇(5/9)

log₇(5) - 2log₇(3)

300

Find the value of the logarithm without a calculator

log₄(8)

3/2

400

Expand the following logarithm

ln(9x)

ln(9) + ln(x)

500

Condense the expression to the logarithm of a single quantity

log(x) − 3 log(y) + 5 log(z) 

log(xz⁵ / y³)

3.4 - Exp and Log Equations

100

Solve for x

ln(x) - ln(11) = 0

x = 11

200

−x²e^-x + 6xe^−x = 0

0, 6

300

7e^−2x/3 = 10

-0.535

400

ln(x + 4) − ln(x − 3) = ln(x)

4.828

500

log(4z) = 3

250

BONUS

100

6^{−7 − x} = 453

-4.63

200

Immediately following an injection, the concentration of a drug in the bloodstream is 300 milligrams per milliliter. After t hours, the concentration is 75% of the level of the previous hour.

Determine the concentration of the drug after 6 hours. (Round your answer to the nearest whole number.)

53

300

A philanthropist deposits $8,000 in a trust fund that pays 6.5% interest, compounded continuously. The balance will be given to the college from which the philanthropist graduated after the money has earned interest for 40 years. How much will the college receive? (Round your answer to the nearest cent.)

$107,709.90

400

Use the One-to-One Property to solve the equation for x. (Enter your answers as a comma-separated list.)

ln(x − 5) = ln 2

7

500

Rewrite the logarithm as a ratio of common logarithms and natural logarithms.

log₆(35)

log(93)/log(3) log(93)/log(3)