Logarithms

Converting Between Exponents and Logs

100

Rewrite the expression as an exponential equation. Log₄64=3

4³=64

200

Rewrite the Exponential equation as a logarithmic expression. 

5³=125

Log₅125=3

300

Convert the following

Log1000=x

10^x=1000

400

Convert the following

7³=343

Log₇343=3

500

Convert the following

Log_xy=z

x^z=y

Change of Base formula

100

Set up the following log using the Change of Base Formula

Log₇475

(log475)/(log7)

200

Convert the following using the change of base formula.

Log₈512

(log512)/(log8)

300

Evaluate the following using the change of base formula. (give a numeric answer) 

log₄64

(log64)/(log4)=3

400

Evaluate the function using the change of base formula 

log₂18

(log18)/(log2)=4.17

500

Evaluate the logarithm

log₁₃58

log58/log13=1.58

Solving Equations

100

log₄x=4

4⁴=256=x

200

Log₃81=x+5

x=-1

300

log(3x-9)=log(x+8)

x=17/2

400

log₅(2x+5)=3

x=60

500

Log₅625=(5x-26)

6=x

Condensing

100

log₅7+log₅6

log₅42

200

3logx-logx²

logx

300

log₃4x+log₃5-log₃x

log₃20

400

2log₇x+log₇15+log₇7

log₇105x²

500

Condense the expression and then evaluate. 

3log₃4-log₃12

log₃(64/12)=1.5

Expanding

100

log₅7x²

log₅7+2log₅x

200

log₅(7x/4)

log₅7x-log₅4

300

log₃(xy)³

3log₃x+3log₃y

400

log(x⁵y⁶/15)

5logx+6logy-log15

500

log(3x²)⁴

4log3+8logx