Answer:
B
Step-by-step explanation:
Using the rules of logarithms
• log [tex]x^{n}[/tex] ⇔ nlogx
• log x + log y ⇔ log(xy)
• log x - log y ⇔ log ([tex]\frac{x}{y}[/tex] )
Given
2log(x + 3) + 3log(x - 7) - 5log(x - 2) - logx²
= log(x + 3)² + log(x - 7)³ - [ (log[tex](x-2)^{5}[/tex] + logx² ]
= log [(x + 3)²(x - 7)³ ] - log [x² [tex](x-2)^{5}[/tex] ]
= log [ [tex]\frac{(x+3)^2(x-7)^3}{x^2(x-2)^5}[/tex] ] → B
