Math

Converting Exponential And Logarithmic forms

100

Convert to Log Form

3⁵= 243

log₃(243)=5

200

Convert to Exponential Form

log₈64=2 

8²=64

300

Convert to Exponential Form

log₂1/16

2^-4=1/6

400

Convert to Log From

14^-2=1/196

log₁₄(1/196)=-2

500

Convert to Log Form

(1/6)³=1/216

log_1/6(1/216)=3

Evaluating Logs

100

Evaluate the Log

log₂^1/8

-3 

200

Evaluate the Log

log₆^1/216

-3

300

Evaluate the Log

log₁₀100

2

400

Evaluate the Log

log₈₁27

0.75

500

Evaluate the Log

log₄3457393653

15.84

Condensing Logarithms

100

Condense this Log

2log₃4

log₃16

200

Condense this Log

2log₂2

2

300

Condense this Log

20log₉8-4log₉11

14.56 or log₉8²⁰/11⁴

400

Condense this Log

10log₆8+5log₆3

14.67 or log₆(3⁵^8¹⁰)

500

log₂11+log₂3/2 + log₂10/2

5.91 or log₂(11\sqrt{30 })

Logarithmic Equations

100

Answer this question.

e⁵=x

about 1.609

200

Answer this question

2e^x=20

ln(10) about 2.303

300

Answer this question 

e^-4x+8=35

x=ln(27)/-4 about -0.824

400

Answer the question

2ln(x)+4=10

x=e³ about 20.086

500

Answer this questions 

ln(x-1)=ln(3x+2)

NO solution

Applications

100

 Answer this problem

We have $10,000 to invest for 44 months. How much money will we have if we put the money into an account that has an annual interest rate of 5.5% and interest is compounded monthly.

12,228.77

200

Answer this question 

We are starting with $5000 and we’re going to put it into an account that earns an annual interest rate of 12%. How long should we leave the money in the account in order to double our money if interest is compounded quarterly.

5.78

300

Answer this question 

A population of bacteria initially has 90,000 present and in 2 weeks there will be 200,000 bacteria present.

1. Determine the exponential growth equation for this population.
2. How long will it take for the population to grow from its initial population of 90,000 to a population of 150,000?

1). P(t)= 90,000e^0.3993t

2). 1.28 weeks

400

Answer these questions 

A population of bacteria initially has 250 present and in 5 days there will be 1600 bacteria present.

1. Determine the exponential growth equation for this population.
2. How long will it take for the population to grow from its initial population of 250 to a population of 2000?

1). Q=250e^1/5ln(32/5)t

2). 5.60

500

Answer these questions 

We initially have 100 grams of a radioactive element and in 1250 years there will be 80 grams left.

1. Determine the exponential decay equation for this element.
2. How long will it take for half of the element to decay?
3. How long will it take until there is only 1 gram of the element left?

1). Q=100e^{1/1250ln(4/5)t}

2). 3882.85

3).25797.1279