What is expand log_{6}((216x^3)/y) ?

The solution to expand log_{6}((216x^3)/y) is 3+3log_{6}(x)-log_{6}(y)

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expand log_{6}((216x^3)/y)

expand

lo g_{6} (\frac{216 x ^{3}}{y})

3 + 3 lo g_{6} (x) - lo g_{6} (y)

Solution steps

lo g_{6} (\frac{216 x ^{3}}{y})

Apply log rule:

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

lo g_{6} (\frac{216 x ^{3}}{y}) = lo g_{6} (216 x^{3}) - lo g_{6} (y)

= lo g_{6} (216 x^{3}) - lo g_{6} (y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{6} (216 x^{3}) = lo g_{6} (216) + lo g_{6} (x^{3})

= lo g_{6} (216) + lo g_{6} (x^{3}) - lo g_{6} (y)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{6} (x^{3}) = 3 lo g_{6} (x)

= lo g_{6} (216) + 3 lo g_{6} (x) - lo g_{6} (y)

lo g_{6} (216) = 3

= 3 + 3 lo g_{6} (x) - lo g_{6} (y)

\frac{1}{20} ln (\frac{31}{20})

ln (2.8246 x 1 0^{- 10})

ln (- iπ)

lo g_{3} (w \cdot u^{6} \cdot v)

ln (12) + ln (2)

What is expand log_{6}((216x^3)/y) ?
The solution to expand log_{6}((216x^3)/y) is 3+3log_{6}(x)-log_{6}(y)