Question 7 of 10For any positive numbers a, b, and d, with b 1,logA. log, a + logodB. log, a-log, dC. d.logbaO D. log, a log, d

Question 7 of 10For any positive numbers a b and d with b 1logA log a logodB log alog dC dlogbaO D log a log d class=

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Answer:

Option B

Explanation:

Given the logarithm expression:

[tex]\begin{gathered} \log_b\left(\frac{a}{d}\right) \\ a,b.d\text{ positive numbers} \\ b\cancel{=}1 \end{gathered}[/tex]

By the quotient law of logarithms:

[tex]$\log _{b}\left(\frac{M}{N}\right)=\log _{b} M-\log _{b} N$[/tex]

Therefore:

[tex]\operatorname{\log}_b\left(\frac{a}{d}\right)=\log_b\left(a\right)-\log_b\left(d\right)[/tex]

Option B is correct.