Logarithms!! :)

solving logarithmic equations

100

log₇14m=log₇(6m-10)

m=-5/4

200

log₃(8x+16)=log₃(5x-7)

m=-23/3

300

log₄8x=2

x=2

400

logb-log8=log5

b=40

500

log₆y+log₆7=1

y=6/7

Exponential equation solving with logs (round to 4 decimal places)

100

10^5x+7+4=12

-1.2194

200

5 x 7^4x+3=21

x=.9344

300

4^5x/7=11

x=.6267

400

e^y+6-24=-12

y=-3.5151

500

4e^2x+12=25

x=-5.0837

writing logs in terms of others

100

log2≈.3,  log5≈.7,  log8≈.9,   log10

1.0

200

log₅2≈.4,  log₅7≈1.2,  log₅9≈1.4,  log₅126

3.0

300

log₇3≈.6,  log₇5≈.8,  log₇6≈.9,  log₇(25/6)

.7

400

log₄7=B,  log₄9=Y,  log₄3=T,  log₄(81/27)

2Y-3T

500

log₉4≈.6,  log₉6≈.8, log₉8≈.9,  log₉(1/24)

-1.4

change of base formula (round to nearest 100th) and the meaning of logs

100

log₂₂17

.92

200

log₁₄32.1

1.31

300

log_x1/4=12

x¹²=1/4

400

22⁵=3/7

log₂₂3/7=5

500

log_5/22Q=72

(5/22)⁷²=Q

Properties of Logs

100

log₇(10 x 7 x 14)

log₇10+log₇7+log₇14

200

log(2 x 4² x 17³)

log2+2log4+3log17

300

log₄(10/22)

log₄10-log₄22

400

log₃X+log₃2

log₃2x

500

4log₈22-4log₈8

log₈(22/8)⁴