What is expand log_{5}(x^3y^6) ?

The solution to expand log_{5}(x^3y^6) is 3log_{5}(x)+6log_{5}(y)

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expand log_{5}(x^3y^6)

expand

lo g_{5} (x^{3} y^{6})

3 lo g_{5} (x) + 6 lo g_{5} (y)

Solution steps

lo g_{5} (x^{3} y^{6})

Apply log rule:

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

lo g_{5} (x^{3} y^{6}) = lo g_{5} (x^{3}) + lo g_{5} (y^{6})

= lo g_{5} (x^{3}) + lo g_{5} (y^{6})

Apply log rule:

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

lo g_{5} (x^{3}) = 3 lo g_{5} (x)

= 3 lo g_{5} (x) + lo g_{5} (y^{6})

Apply log rule:

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

lo g_{5} (y^{6}) = 6 lo g_{5} (y)

= 3 lo g_{5} (x) + 6 lo g_{5} (y)

lo g_{6} (- 2 lo g_{10} (y))

ln (\frac{x}{y - z})

4 ln (\frac{36}{35}) - 0.05

ln (3 u) - ln (u)

lo g_{2} (\frac{1}{0.2}) + 1

What is expand log_{5}(x^3y^6) ?
The solution to expand log_{5}(x^3y^6) is 3log_{5}(x)+6log_{5}(y)