Logarithm Review

Common Bases

100

log₁₀100

2

200

log₂16

4

300

log₃81

4

Laws of Logs

100

log(10*100)

1+2=3

200

log(100/10)

2-1=1

300

log(10³)

3*1=3

400

log₅(25*125)

2+3=5

500

log₃(243/9)

5-2=3

Change of Base

100

log₂8

using base 10

log₂8 =  (log 8)/log 2 =0.903/0.301~~3 

200

log₃81

log₃81 =  log81/log 3=1.908/0.477~~4 

300

log₇1000

log₇1000 =  log 100/log7=3/0.8451~~3.55 

400

log₄64

log₄64 =  log64/log4 = 1.806/0.602~~4 

500

log₆500

log₆500 =  log 50/log 6= 0.699/0.778~~3.77 

Inverse Exponents

100

2^x = 8

x = log₂8

   = 3   (since 2³ = 8)

200

10^x = 1000

x = log₁₀1000

   = 3 (since 10³ = 1000)

300

5^x = 625

x = log₅625

   = 4

400

3^x = 50

x = log₃50 

   =  log50/log3 

    ~~ 3.56 

500

7^2x-1 = 150

log(7)*(2x-1) = log(150)

2x - 1 =  log150/log7 ~~2.576 

     2x = 3.576

      x  ~~  1.79