Chapter 7 - Logarithms.

Converting Log and Exponential Form

100

Convert to Exponential Form:

log_2(8)=x

2^x=8

200

Convert to Logarithmic Form:

4^y=x

log_4(x)=y

300

Convert to Exponential Form:

log_(x-1)(4)=2y

(x-1)^(2y)=4

400

Convert to Exponential Form:

log_(3x)(5-z)=4y

(3x)^(4y)=5-z

or

500

Convert to Logarithmic Form:

10^(x+4)=2y-7

log(2y-7)=x+4

Interpreting Exponential Functions

100

Estimate:

 log₂21

4.39

200

Is the function exponential growth or decay?

y=3(2.5)^x

Exponential Growth 

300

Estimate:

log₃7

Between 1 and 2

400

Everleigh won $2,500 and deposited it into a savings account earning 4.2% interest compounded annually. How much was in the account after 10 years?

$3,772.40

500

Suppose you invest $3000 at an annual interest rate of 7.68%.How much money will be in the account after 15 years compounded semi-annually?

$9,290.98

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100

Condense the Logarithms:

log_3(2x)-log_3(5y)

log_3((2x)/(5y))

200

Completely Expand the Logarithm:

log((2x)/y)

log(2)+log(x)-log(y)

300

Condense the Logarithms:(use ln the same as any other log)

2log(3)+4log(y)-2log(x)

log((9y^4)/x^2)

400

Condense the Logarithms:

3log(x)+3log(3)-(4log(2)+ 5log(z))

log((27x^3)/(16z^5))

500

Completely Expand the Logarithm:

log((3x^6y^7)/(7z^5))

log(3)+6log(x)+7log(y)-(log7+5log(z))

Solving Log Equations

100

Solve using Logarithms:

log_7(2x) = log_7(x+3)

x=3

200

Solve Using Logarithms:

log_3(1/27)=x

x= -3

300

Solve by Converting:

log_4(x)=-3

x=

x = 1/64

400

Solve using Logarithms:

 

log(x+1) = 2

 x = 99

500

Solve using Logarithms:

log(5)-log(2x)=1

x=1/4

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100

Solve the equation with common bases:

3^(2x)=27

x=3/2

200

Solve the equation using common bases:

3^(x+2)=27^(2x)

x=2/5

300

Solve the equation using logarithm. Round to the hundredths place.

4^x=19

x=2.12

400

Solve the equation. Round to the tenths place.

2^(3x-4)=5

x=2.1

500

Solve the equation. Round to the hundredths place.

6^(2x)-2=8

x=0.64