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-1)(4)=2y

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

400

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:

5^(2x)=21

x=log_5(21)/2

200

Solve for x:

5*2^x=240

x=log_2(48)

300

Solve for x:

2*3^(x-5)=12

x=log_3(6)+5

400

Solve for x:

 2*e^(3x-1)-7=13

 x=(ln10+1)/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)

ln(3)-ln(x)+ln(y)

ln((3y)/x)

400

Condense the Logarithms:

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

log((3x)/(2z))

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_2(x)=-5

x=

x = 1/32

400

Solve using Logarithms:

 

log_x(1/64) = -2

 x = 8