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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]
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