Math is Fun Midterm Project Logarithms

Converting Exponential into Logarithmic and Logs into Exponential

100

log₈4096=4

8⁴=4096

200

27^1/3=3

log₂₇3=1/3

300

log₅1/5=-1

5^-1=1/5

400

9³=729

log₉729=3

500

3^-5=1/243

log₃1/243=-5

Condensing Logs

100

2log₆7 + 3log₆3

log₆1323

200

7log₇p-8log₇q

log₇p⁷/q⁸

300

log₂64-1/3(5log₂3+log₂7)

log₂64/567

400

log70-4log4

log 70/256

500

1/3ln27 + 4ln3 

ln243

Expanding Logs

100

logv⁷w⁵/u³

7logv+5logw-3logu

200

ln(cd⁸)

lnc+8lnd

300

log₈(6t³s³)⁵

5log₈6+15log₈t+15log₈s

400

ln(k⁹/l⁵)

9lnk-5lnl

500

log₄(7⁴k²t¹¹s⁶)²

8log₄7+4log₄k+22log₄t+12log₄s

Solving Logarithmslog()=log()

100

ln(5x-3)=ln(2x+6)

x= none 

x=3 is extraneous 

200

log₃5+log₃(6x-2)=log₃49

x=1.97

300

1/2log(4t²)=log(5t-2)

t=2/3

400

2log(c+2)=log100-log25

c=0

500

log₂10p=log₂8

x=4/5

Solving Logarithmslog()=number

100

ln(6x-9)=5

e⁵+9/6

200

log₂(k-5)+log₂(k+6)=7

No solutions

both -6 and 5 are extraneous 

300

log₅(k+6)-3=1

k=614

400

3 log₂(3x+1)-3=6

x=10.3

500

ln5c=15

c=e¹⁵/5