Log functions

Re Write Log

100

log₅25=2

5²=25

200

log₁₆256=2

16²=256

300

log₂₃1=0

23⁰=1

400

log₁₅1/225=-2

15^-2= 1/225

500

64^1/2=8

log₆₄8=1/2

Re Write Base E

100

e⁴ = x

4 = lnx

200

e^x = 24

x = ln 24

300

e^x-10= 50

x-10 = ln 50

400

ln 87 = x

87 = e^x

500

ln 37 = x+5

37 = e^x+5

Equation Rules

100

log₇10 - log₇3

log₇ 10/3

200

log₄(xy)

log₄x + log₄y

300

log₉a+log₉b+5log₉c

log₉(bac⁵)

400

log₃(z⁴x^1/2)

4log₃z + 1/2log₃x

500

log₇(x³y)⁴

12log₇x + 4log₇y

Base E Equations

100

ln(x+3) = ln(2x-10)

13

200

3 x 10^n-8 = 43

9.156

300

18^-r + 4.4 =103

-1.588

400

ln (x-8) - ln4 = 1

4e+8

500

ln(x²-9) - ln8 = ln 2

5,-5

Log Equations

100

log (5m+7) = log (3m+9)

m = 1

200

 log (5-5x) + log 2 = log (9-3x)

1/5

300

log₂4x+log₂6 = 3

1/3

400

log₄8 - log₄-x = 5

-1/128

500

 log 8 + log(x²-1) = 1

3/2 and -3/2