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:

log4=2y

10^(2y)=4

400

Convert to Logarithmic Form:

2^(x+4)=y

log_2(y)=x+4

500

Convert to Exponential Form:

ln(5)=4y

e^(4y)=5

Solving Exponential Equations

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 or 6.63

500

Solve for x:

 e^(3x)-7=23

(ln(30))/3 or 1.13

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)+2log(y)-5log(z)

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

2

200

Solve Using Logarithms:

log_3(1/27)

-3

300

Solve by Converting:

log_4(10)

1.66

400

What is x?

 

log_x(64) = 3

 x = 4

500

Solve using Logarithms:

log_9 27

x=3/2