Question

Find the value of $\left( {\log 5 + \log 8 - 2\log 2} \right)$ is equal to
A) 1
B) 2
C) 0
D)-3

Answer 1

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]