use the properties of the logarithms to write each expression as a single term

Question

A) log(x^(2)-2x) + log (base 5) x^(-1)

B) ln (x^(2)-25)-ln (x+5)

Answer 1

B) ln (x^(2) - 25) - ln (x+5)

= ln {x^(2) - 5^(2)} - ln (x+5)

formula : a^2 - b^2 = (a+b)(a-b)

= ln{(x+5)(x-5)} -  ln (x+5)

Apply formula : ln(a) - ln(b) = ln(a/b)

= ln {(x+5)(x-5)} / (x+5)

= ln (x-5)

The solution is  ln (x-5)

 

 

Answer 2

A) log(base 5)(x^2 - 2x) + log(base 5)x^(-1)

Apply formula : log(a) + log(b) = log(a*b).

= log(base 5){(x^2 - 2x)*x^(-1)}

= log(base 5)[(x^2 - 2x) / x ]

= log(base 5)[x(x - 2) / x]

Cancel common terms.

log(base 5)(x - 2)

The solution is log(base 5)(x - 2)