What is expand log_{6}(x^4y^3) ?

The solution to expand log_{6}(x^4y^3) is 4log_{6}(x)+3log_{6}(y)

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expand log_{6}(x^4y^3)

expand

lo g_{6} (x^{4} y^{3})

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

Solution steps

lo g_{6} (x^{4} y^{3})

Apply log rule:

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

lo g_{6} (x^{4} y^{3}) = lo g_{6} (x^{4}) + lo g_{6} (y^{3})

= lo g_{6} (x^{4}) + lo g_{6} (y^{3})

Apply log rule:

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

lo g_{6} (x^{4}) = 4 lo g_{6} (x)

= 4 lo g_{6} (x) + lo g_{6} (y^{3})

Apply log rule:

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

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

= 4 lo g_{6} (x) + 3 lo g_{6} (y)

lo g_{a} (0.78) - lo g_{a} (6)

\frac{3}{4} lo g_{2} (x^{4}) - lo g_{2} (y)

- ln (\frac{2}{2}) + ln (1)

ln (\frac{x ^{4}}{( 3 x - 4 ) ^{2}})

\frac{1}{10} ln (\frac{10}{7})

What is expand log_{6}(x^4y^3) ?
The solution to expand log_{6}(x^4y^3) is 4log_{6}(x)+3log_{6}(y)