Question

please solve this question

Answer 1

Main operations in this problem that we are going to use:
1. log a - log b = log(a/b)
2. log a + log b = log (ab)

Given log₁₀(x-4)-log₁₀(3x-12)+log₁₀(1/x)
        = log₁₀(x-4)-log₁₀(3{x-4})+log₁₀(1/x)
        = log₁₀[(x-4)/3(x-4)]+log₁₀(1/x)
        = log₁₀(1/3)+log₁₀(1/x)
        = log₁₀(1/3x)
        

Answer 2

Notation: log a means log a with base 10

log(x-4) - log(3x-12) + log(1/x)
=log (x-4) - log(3(x-4)) + log(1/x)

[
Now, log (a×b) = log a + log b
So, log(3(x-4)) = log 3 + log (x-4)
]
So, log(x-4) - log(3(x-4)) + log(1/x)
= log(x-4) - [log 3 + log (x-4) ] + log (1/x)
= log(x-4) - log 3 - log(x-4) + log(1/x)
= log(1/x) - log 3
= log(1/3x)

[
As log a - log b = log (a/b)
]