Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Use [tex]$\log _{ b } 9 = 2.197$[/tex] and/or [tex]$\log _{ b } 8 = 2.079$[/tex] to find [tex]$\log _{ b } \frac{9}{8}$[/tex].

[tex]\[
\log _b \frac{9}{8} = \boxed{\phantom{aa}}
\][/tex]

(Simplify your answer.)

Sagot :

GinnyAnswer
To solve for [tex]\(\log_b \frac{9}{8}\)[/tex] given [tex]\(\log_b 9 = 2.197\)[/tex] and [tex]\(\log_b 8 = 2.079\)[/tex], we can use the logarithm quotient rule, which states that [tex]\(\log_b \left(\frac{a}{c}\right) = \log_b a - \log_b c\)[/tex].

Given:
[tex]\[ \log_b 9 = 2.197 \][/tex]
[tex]\[ \log_b 8 = 2.079 \][/tex]

We want to find [tex]\(\log_b \frac{9}{8}\)[/tex]. According to the logarithm quotient rule, we can write:

[tex]\[ \log_b \frac{9}{8} = \log_b 9 - \log_b 8 \][/tex]

Substitute the given values:

[tex]\[ \log_b \frac{9}{8} = 2.197 - 2.079 \][/tex]

Now, perform the subtraction:

[tex]\[ 2.197 - 2.079 = 0.118 \][/tex]

Thus, the simplified answer is:

[tex]\[ \log_b \frac{9}{8} = 0.118 \][/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.