Question

Rewrite the following expression as a single logarithm:

Answer 1

The answer is $log( \frac{ (x+3)^{2}(x-2)^{5} }{ (x-7)^{3} x^{2} } )$

2log(x + 3) - 3log(x - 7) + 5log(x - 2) - log(x²)

a*log(x) = log(xᵃ)
2log(x + 3) = log((x + 3)²)
3log(x - 7) = log((x - 7)³)
5log(x - 2) = log((x - 2)⁵)

2log(x + 3) - 3log(x - 7) + 5log(x - 2) - log(x²)
= log((x + 3)²) - log((x - 7)³) + log((x - 2)⁵) - log(x²)

log(a) - log(b) = log(a/b)
log(a) + log(b) = log(ab)
log((x + 3)²) - log((x - 7)³) + log((x - 2)⁵) - log(x²) = $log( \frac{ (x+3)^{2}(x-2)^{5} }{ (x-7)^{3} x^{2} } )$

Answer 2

Answer:

log((x+3)^2(x-2)^5 / (x-7)^3 x^2)

Step-by-step explanation:

the one with the 5 exponet at the end of top row