Question

log8-2log6+log3

Answer 1

couple logarithm rules (with logs with same bases)

\(\Large\color{black}{ \bf log(a) +log(b)= log(a\times b)}\)

\(\Large\color{red}{ \bf log(v) -log(f)= log(v\div f)}\)

Answer 2

Before you apply these rules,

\(\Large\color{green}{ \bf r~log(w) =log(w^{r})}\)
(apply this to the second log in your equation.

Answer 3

so log 8/36?

Answer 4

\(\Large\color{purple}{ \bf log(8)-2log(6)+log(3) }\)

apply the green rule,

\(\Large\color{purple}{ \bf log(8)-log(6^{2})+log(3) }\)

\(\Large\color{purple}{ \bf log(8)-log(36)+log(3) }\)

apply the red rule,

\(\Large\color{purple}{ \bf log(\frac{8}{36})+log(3) }\) simplify,

\(\Large\color{purple}{ \bf log(\frac{2}{9})+log(3) }\)

apply the black rule.

\(\Large\color{purple}{ \bf log(\frac{2}{9} \times 3) }\)

\(\Large\color{purple}{ \bf log(\frac{2\times 3}{9} ) }\)

\(\Large\color{purple}{ \bf log(\frac{6}{9} ) }\)

\(\Large\color{purple}{ \bf log(\frac{2}{3} ) }\)

Answer 5

got it thanks

Answer 6

You welcome !