LOGARITHMS 1

 Simplify Log₂128 – Log₅3125 – Log₆7776

 

Solution

 

= Log₂128 – Log₅3125 – Log₆7776

 

= Log₂2⁷ – Log₅5⁵ – Log₆6⁵

 

= 7Log₂2 – 5Log₅5 – 5Log₆6  because Log_aaⁿ =  nLog_aa

 

= (7 x 1) – (5 x 1) – (5 x 1)    

 

= 7 – 5 - 5

= 7 – 0

 

= 7

 

Hence Log₂128 – Log₅3125 – Log₆7776 = 7 

 

TRY THIS…………..

 

Simplify Log₂2048 – Log₃243 – Log₅3125

SIMPLIFY

 Simplify 44

               8^-4/3

 

Solution

 

=  44

    8^-4/3

 

= 44 x 1

           8^-4/3

 

=  44 x 8^4/3        [Since 1/a^-n = aⁿ]

 

=  44 x (8^1/3)⁴        [Since 8^1/3 = cube root of 8 = 2]

 

=  44 x (2)⁴        

 

=  44 x 16

 

= 704     

          

Hence   44        = 704

              8^-4/3

 

TRY THIS…..

simplify 24

              64^-2/3

 

X-INTERCEPT

 If 3x + 7y - 56 = 0; find x-intercept.

Solution

x-intercept is when y=0.

3x + 5y -56 = 0

3x + 5(0) - 56 = 0

3x - 56 = 0

3x = 0+ 56

3x = 56

3      3

 

x= 56/3

Hence x-intercept= 56/3 

TRY THIS………..

If 11x - 7y - 30 = 0; find x-intercept.

LOGARITHMS

If log 2= 0.3010; find the value of log 12500 without using tables.

Solution

=log12500

=log(100,000 ÷8)

=log100,000 –log8

= log10⁵ - log2³

= 5log10 - 3log2

=(5 x 1) - (3 x 0.3010)

= 5  -  0.9030

=4.097

Hence log 1250 =4.097  

TRY THIS……………

If log 2= 0.3010; find the value of log 25,000 without using tables.