Answer:
[tex] \log(150) [/tex]
Step-by-step explanation:
We want to rewrite the following as a single logarithm:
[tex]2 - log(6) - log(9) [/tex]
We introduce logarithm in the first term to get:
[tex]2 \log(10) - \log(6) - \log(9) [/tex]
Recall that:
[tex] log(a) - log(b) = \log \frac{a}{b} [/tex]
We apply this property to get:
[tex]2 log(10) - log( \frac{6}{9} ) [/tex]
This gives:
[tex] log( {10}^{2} ) - log( \frac{6}{9} ) [/tex]
[tex]log( {100}) - log( \frac{2}{3} )[/tex]
[tex] log( \frac{100}{ \frac{2}{3} } ) = log( \frac{300}{2} ) = log(150) [/tex]
