Evaluate log5(\( y^2x^5 \div 125b½) \)
A
2 log5y + 5log5 y2 − 3
B
log5 y2 + 5log5 x + 3
C
25logy 5 + 3
D
2log5y + 5log5x − ½ log5b −3
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\log_{5}(y^{2} x^{5} \div 125b^{\frac{1}{2}})\)
= \(\log_{5} y^{2} + \log_{5} x^{5} - [\log_{5} 125 + \log_{5} b^{\frac{1}{2}}\)
= \(2\log_{5} y + 5\log_{5} x - \log_{5} 5^{3} - \frac{1}{2} \log_{5} b\)
= \(2\log_{5} y + 5\log_{5} x - 3 - \frac{1}{2}\log_{5} b\)
Source: Myschool Past Questions Archive (Record #40741)