Question

Using log table, find the value of 0.09634^2​

Answer 1

Step-by-step explanation:

How do I solve this equation using log tables?

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We will solve it partwise.

First of all let us suppose,

(35.285)^2 = a

Taking log of both sides

2 log (35.285) = log a

3.0952 = log a

Now taking antilog

antilog (3.0952) = a

=> 1245.09 = a ........(i)

Similarly let us suppose

(23..45)^3 = b

Taking log we get

4.1104 = log b

Now take antilog

12895.3 = b .........(ii)

Adding (i) and (ii)

We get value of expression inside cube root.

Now let us suppose (a+b)^1/3 = x

=> (14140.39)^1/3 = x

Taking log

1/3 log (14140.39) = log x

=> 1.3835 = log x

Now take antilog to get value of x.

X = 24.182

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Given: Log/AntiLog tables

Given equation: x^3 = (35.285)^2 + (23.45)^3

x^3 = a + b

here

a = (35.285)^2

b = (23.45)^3

take log on both sides [Assume base is 10]

log(a) = 2 log(35.285) = 2 (1.5476) = 3.0952

a = antilog (3.0952) = 1.246 × 10^3 = 1246

same for b

log(b) = 3 log(23.45) = 3(1.3701) = 4.1103

b = antilog (4.1103) = 1.289 × 10^4 = 12890

x^3 = a+b

x^3 = 1246 + 12890 = 14136

Again, take log on both sides

3log(x) = log(14136) = 4.1501

log(x) = 4.1501 / 3 = 1.3834

x = antilog(1.3834) = 24.17