FINDING LOGARITHMS WITHOUT USING TABLE

By Esther Gift






FINDING LOGARITHMS WITHOUT USING TABLES.



Example 1:

log₁₀2 = 0.3010 and log₁₀3 = 0.4771. Evaluate log₁₀4.5

Solution:

log₁₀4.5 = 

log₁₀45/10 = 

log₁₀9/2 = log₁₀9 - 

log₁₀2 

= log₁₀3² - 

log₁₀2 = 2 x 0.4771 - 

0.3010 

= 0.6532


Example 2:


if log₁₀2 = 0.30103, find without using logarithms tables the number of digit in 2⁶⁴ 

Solutions:

2⁶⁴ = y

log₂y = 64

logy/log2 = 64
logy/ 0.30103 =64
64 x 0.30103 = logy
10¹⁹·²⁶⁵⁹ = 20





Example 3:

Given that log₁₀5 = 0.6990 and log₁₀7 = 0.8451. Without using tables, find the value of log₁₀140. Hence, solve x⁰·⁹⁶⁴¹ = 140

Solution:


log₁₀140 = log₁₀700/5 = log₁₀700 - log₁₀5 = 
log₁₀ 7 x 100 - log₁₀5=
log₁₀7 + log₁₀10  - log₁₀5 
substitute the logs into the equation 
= 0.8451 + 2 - 0.6990 = 2.1461

Hence,     x⁰·⁹⁶⁴¹ = log₁₀140 ⇒ take log of both side
log₁₀x⁰·⁹⁶⁴¹ = log₁₀140

0.9641log₁₀x = 2.1461
log₁₀x = 2.1461
              ------------
              0.9641
          = 2.1461
x = 10²·²²⁶⁰ 
x = antilog of 2.2260
x = 168.27



Example 4:

Given that log₁₀2 = 0.30103, and log₁₀3 = 0.47712

Evaluate log₁₀15

Solution :

log₁₀15 = log₁₀30/2 = log₁₀30 - log₁₀2
= log₁₀3 x 10 - log₁₀2
= log₁₀3 + log₁₀10 - log₁₀2
= 0.47712 + 1 - 0.30103 = 1.17609


Example 5:

If log₅ = 0.6990, and 10ʸ = 0.05, Find the value of y

Solution:
10ʸ = 0.05 ⇒ take log of both side
log10ʸ = log0.05

y log10 = log0.05

y log10 = log5/100
ylog10 =log5 - log10²

y x1 = 0.6990 - 2log10

y = 0.6990 - 2 x1

y = 0.6990 - 2



Example 6:

Simplify each of the following
a.  log₆₄0.125    

 b.   log₁₀25 +      

       log₁₀32 - log₁₀8
     



Solutions:


(a) log₆₄0.125

  =  log0.125/log64

=  log125/1000 ÷ log64 

log8 ÷ log64
log8/log64

log2³/log2⁶

3log2/6log2

log2 cancled log2
=3/6 = 1/2


(b).  log₁₀25 +log₁₀32 +log -log8

log₁₀(25 x 32 )/8

log₁₀100 = log₁₀10² = 2log₁₀10 = 2 x1 = 2

Example 7:

If log₆4=z, log₅6 = y, Express the following in term of x and y

i.   log₆64


solution

i.    log₆64 = log₆4³ = 3log₆4 = 3 x z= 3z


ESTHER GIFT is an ethusaitic and dynamic coach with great affinity for young minds and Students. She is a violence reader, who believes so much in her prowess to transmute a penetrating influence in the young ones and students. She has tremendously impacted lives across the globe through her articles with the use of scientific assertions and life tested principles that are bold enough to accelerate man beyond the sky of limitations. Her wealth of knowledge and passion is seen in DÆGESEAGE her company. SMS - STUDENTS' MONTHLY SERIES- a golden give away by DÆGESEAGE has massively reach and change lives amazingly. She was awarded recently by MINDCITY for excellence . In her vision to raise leaders she set up an annually quadrant LEADERSHIP AND EMPOWERMENT FORUM where she mentor upcoming leaders on how to lead with a privilege to master a handfull skill. Her vision lies in the young minds and students.Her aspirations is to lead them to a point of global relevance

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