Question

Simplify the following expression log(25x^3) +3log(1/x)

Answer 1

The simplified form is
`\log 25`

Explanation:

We need to simplify the given expression

Given:-
`log(25x^(3)+3log((1)/(x))`

According to laws of logarithm :
`b \log a = \log a^(b)`

So,
`3 \log ((1)/(x)) = \log ((1)/(x^(3)))`

According to laws of logarithm :
`\log a + \log b = \log a* b`

So,
`\log 25x^(3) + \log ((1)/(x))^(3) = \log 25x^(3)* ((1)/(x^(3)))`

`=\log ((25x^(3))/(x^(3)))}`

`=\log 25`

Therefore, the simplified form is
`\log 25`

Answer 2

= ㏒25

Explanation:

log25x³ + 3log1/x

According to one of of the laws of logarithm which states : b log a = log a^b

So, 3 log 1/x = log (1/x)³

Another law states that : log a + log b = log a * b

So, log 25x³ + log (1/x)³ = log (25x³) * (1/x)³

log (25x³)/x³

= log 25