Question

If log 10 2 = p, then the value of log 10 5 is

Answer 1

Answer:

log(5) base 10 =log(10/2) base 10

=log(10)-log(2)=1-log(2)

log(2)=0.3010

=> log(10)=1–0.3010=0.699

the property used here is that

log(a/b)=log(a)-log(b)

also to find log(2) you can find value of -log(1/2)

and use expansion

note:it will give you answer in base e(2.71828…)

log(1+x)=x - (x^2)/2 + (x^3)/3 + …(add infinitely)

you can add up to 5–6 terms to get a nice estimate(take x=-1/2)

note:this series only gives answer if |x|<1. So we can't directly get the value of log(2).

now we can use that value to get a estimate value of log(1/2) in base 10

(log(x) base e = 2.303 ×log(x) base 10)

and hence we can get the value of log(2) by this

Answer 2

Given : log₁₀ 2 = p  

To Find : Value of log₁₀5

Solution:

as we know that logₐa= 1

hence log₁₀10  = 1

=> log₁₀(2x5)  = 1

log ab  = log a + log b

=> log₁₀2 +  log₁₀5  = 1

log₁₀ 2 = p  

=> p + log₁₀5  = 1

=> log₁₀5  = 1 - p

log₁₀5  = 1 - p

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