Chapter 5b - 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

Solving Algebraic Log Equations with Log Properties

100

Solve for x:

 log_x216=3

 x=6

200

Solve for x:

log_3(x-3)=2

x=12

300

Solve for x:

log_4(2)+log_4(x+6)=1

x=-4

400

Solve for x:

4log_9(3)-log_9(x)=2

x=1

500

Solve for x:

log_2(8x)-3log_2(4)= 3

x=64

Expanding/Condensing Logarithms

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))

Evaluating Logs

100

Solve using Logarithms:

log_7(49) = x

x=2

200

Solve Using Logarithms:

log_3(1/27)=x

x= -3

300

Solve by Converting:

log_4(x)=-5

x=

x = 1/1024

400

Solve using Logarithms:

 

log_x(1/64) = -2

 x = 8

500

Solve using Logarithms:

log_25(5)=x

x=1/2