Question

1. If log10 2 = p, then the value of log10 5 is​

Answer 1

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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Answer 2

SOLUTION

GIVEN

$\sf{ log_{10}2 = p }$

TO DETERMINE

$\sf{ log_{10}5 }$

EVALUATION

$\displaystyle \: \sf{ log_{10} 5 }$

$\displaystyle \: \sf{ = log_{10} \bigg( \frac{10}{2} \bigg) }$

$\displaystyle \: \sf{ = log_{10} 10 - log_{10}2 }$

$\displaystyle \: \sf{ =1 - p}$

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