Logarithmic equations

Logarithmic equations

1. Product

   • LogbM + logbN=Logb (M*n)
   • Log3 (9) + Log3 (27)
     • Write number in exponential form.
     • Log3 (3^2) + log3 (3^3)
       • Using loga (a^x) =X
       • 2+3
         • Just add them together. Seriously just add.
         • 5
   • Log 9+Log 27 33 9*27=243 Multiply 9 and 27 Log 243=5 3 3 to the fifth power is 243
     • Log 8+Log 16 8*16=128 Multiply 8 and 16 Log 128=7 to the seventh power is 128
       • Log 80+Log 125 10 10 80*125=10,000 Multiply 80 and 125 Log 10,000=4 10 10 to the fourth power is 10,000
     • Solving algebraically example:
       • Log X^5=20 4 5/5*log X=20/5 4 Log X=4 4 4^4=X 256

2. Quotient.

   • Log2 (80)-Log2(10)
     • Calculate the difference of logarithms.
     • Log2 (8)
       • Write number in exponential form.
       • Log2 (2^3)
         • Using loga (a^x)=X
         • 3
     • Divide 80/10
   • Log 80-Log 10 22 80/10=8 Divide 80 and 10 Log 8=3 2 2 to the third power is 8
     • 44 384/6=64 Divide 384 and 6 Log 64=3 4
       • 3. Log 10 400/40=100 Divide 400 and 40 4000-Log 40 10 Log 100=2 10 10 to the second power is 100

3. Power property

   • Log 8^5 8 5*log^8 move the 5 8 5*1=5
     • Log 9^4 3 4*log^9 move the 4 3 4*2=8

4. Equality property

   • 1. 7^log7 30 B:7 E:Log 30 7 X=Log 30 7 X= 30
     • 12^log12 1 B:12 E:log 1 12 Log X=log 1 12. 12 X=1

5. Important equations: Log (Solution )=Exponent Base Base^Exponent=Solution