Logarithms Review

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)(4)=2y

(x)^(2y)=4

400

Convert to Logarithmic Form:

2^(x+4)=y

log_2(y)=x+4

500

Convert to Exponential Form:

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

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

Solving Algebraic Log Equations with Log Properties

100

Solve for x:

5^(2x)=25

x=1

200

Solve for x:

5*2^x=240

log_(2)(48)

300

Solve for x:

3^(2x)=27

x=3/2

400

Solve for x:

2*3^(x-5)=12

log_(3)(6)+5

500

Solve for x:

2^(3x)-7=13

(log_(2)(20))/3

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

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

400

Condense the Logarithms:

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

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

500

Completely Expand the Logarithm:

log_7((3x^6y^7)/(z^5))

log_7(3)+6log_7(x)+7log_7(y)-5log_7(z)

Evaluating Logs

100

Solve using Logarithms:

log_7(49) = x

x=2

200

Solve Using Logarithms:

log_3(1/27)=

x= -3

300

Solve by Converting:

log_4(x)=-5

x = 1/1024

400

Solve using Logarithms:

 

log_x(1/64) = -2

 x = 8

500

Solve using Logarithms:

log_(x+2)(16)=2

x=2