# Find the value of $\left( {\log 5 + \log 8 - 2\log 2} \right)$ is equal to

A) 1

B) 2

C) 0

D)-3

Last updated date: 15th Mar 2023

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Answer

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Hint: we are going to solve this problem by using basic logarithmic formulae.

Let the given expression be$x = \log 5 + \log 8 - 2\log 2$

$ \Rightarrow x = \log 5 + \log 8 - \log {2^2}$

$ \Rightarrow x = \log 5 + \log \left( {\frac{8}{4}} \right)$

$ \Rightarrow x = \log 5 + \log 2$

$ \Rightarrow x = \log (5 \times 2)$

$\therefore x = \log 10 = 1$

Note: we used the properties:

$\log {X^y} = y\log x$ ,

$\log X - \log Y = \log \frac{X}{Y}$

$\log X + \log Y = \log (X \cdot Y)$

We know that the value of log 10 = 1. [For natural logarithm]

Let the given expression be$x = \log 5 + \log 8 - 2\log 2$

$ \Rightarrow x = \log 5 + \log 8 - \log {2^2}$

$ \Rightarrow x = \log 5 + \log \left( {\frac{8}{4}} \right)$

$ \Rightarrow x = \log 5 + \log 2$

$ \Rightarrow x = \log (5 \times 2)$

$\therefore x = \log 10 = 1$

Note: we used the properties:

$\log {X^y} = y\log x$ ,

$\log X - \log Y = \log \frac{X}{Y}$

$\log X + \log Y = \log (X \cdot Y)$

We know that the value of log 10 = 1. [For natural logarithm]

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