What is 3log_{9}(x)-18log_{9}(y) ?

The solution to 3log_{9}(x)-18log_{9}(y) is log_{9}((x^3)/(y^{18)})

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simplify 3log_{9}(x)-18log_{9}(y)

simplify

3 lo g_{9} (x) - 18 lo g_{9} (y)

lo g_{9} (\frac{x ^{3}}{y ^{18}})

Solution steps

3 lo g_{9} (x) - 18 lo g_{9} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{9} (x) = lo g_{9} (x^{3})

= lo g_{9} (x^{3}) - 18 lo g_{9} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

18 lo g_{9} (y) = lo g_{9} (y^{18})

= lo g_{9} (x^{3}) - lo g_{9} (y^{18})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{9} (x^{3}) - lo g_{9} (y^{18}) = lo g_{9} (\frac{x ^{3}}{y ^{18}})

= lo g_{9} (\frac{x ^{3}}{y ^{18}})

ln (\frac{5 x}{y ^{2}})

\frac{1}{3} ln (\frac{1}{27})

ln (3 x) + 1

lo g_{e} (22)

5 lo g_{7} (a) + 10 lo g_{7} (b)

What is 3log_{9}(x)-18log_{9}(y) ?
The solution to 3log_{9}(x)-18log_{9}(y) is log_{9}((x^3)/(y^{18)})