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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

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^{6})

Apply log rule:

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

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

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

4 ln (x) - \frac{1}{8} ln (y)

lo g_{2} (x) + 5 lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{10} (\frac{x ^{2}}{2})

\frac{1}{2} ln (x + 1) - \frac{1}{4} ln (x^{2} + 1)

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