What is expand log_{2}(x^6y^4) ?

The solution to expand log_{2}(x^6y^4) is 6log_{2}(x)+4log_{2}(y)

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expand log_{2}(x^6y^4)

expand

lo g_{2} (x^{6} y^{4})

6 lo g_{2} (x) + 4 lo g_{2} (y)

Solution steps

lo g_{2} (x^{6} y^{4})

Apply log rule:

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

lo g_{2} (x^{6} y^{4}) = lo g_{2} (x^{6}) + lo g_{2} (y^{4})

= lo g_{2} (x^{6}) + lo g_{2} (y^{4})

Apply log rule:

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

lo g_{2} (x^{6}) = 6 lo g_{2} (x)

= 6 lo g_{2} (x) + lo g_{2} (y^{4})

Apply log rule:

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

lo g_{2} (y^{4}) = 4 lo g_{2} (y)

= 6 lo g_{2} (x) + 4 lo g_{2} (y)

3 lo g_{5} (x + 2) - lo g_{5} (x)

ln (6 + x) - ln (x)

- lo g_{10} (9.2 \cdot 1 0^{- 6})

ln (\frac{4 x ^{2} + 4 x + 8}{x ^{\frac{4}{3}} tan ( x )})

\frac{1}{4} ln (\frac{5}{3}) + \frac{1}{4} ln (5)

What is expand log_{2}(x^6y^4) ?
The solution to expand log_{2}(x^6y^4) is 6log_{2}(x)+4log_{2}(y)