What is expand log_{10}(x^3y^2) ?

The solution to expand log_{10}(x^3y^2) is 3log_{10}(x)+2log_{10}(y)

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expand log_{10}(x^3y^2)

expand

lo g_{10} (x^{3} y^{2})

3 lo g_{10} (x) + 2 lo g_{10} (y)

Solution steps

lo g_{10} (x^{3} y^{2})

Apply log rule:

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

lo g_{10} (x^{3} y^{2}) = lo g_{10} (x^{3}) + lo g_{10} (y^{2})

= lo g_{10} (x^{3}) + lo g_{10} (y^{2})

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= 3 lo g_{10} (x) + lo g_{10} (y^{2})

Apply log rule:

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

lo g_{10} (y^{2}) = 2 lo g_{10} (y)

= 3 lo g_{10} (x) + 2 lo g_{10} (y)

ln (28) - 2 ln (3) + 7

\frac{1}{2} ln ∣ x + 1 ∣ + \frac{3}{2} ln ∣ x - 1 ∣

lo g_{10} ((\frac{x ^{4}}{( x ^{2} + 1 ) ^{\frac{1}{3}}}) (x - 1)^{2})

\frac{1}{3} ln (8) - 2 ln (2) - \frac{1}{3} ln (5)

lo g_{10} (x) - 3 lo g_{10} (p)

What is expand log_{10}(x^3y^2) ?
The solution to expand log_{10}(x^3y^2) is 3log_{10}(x)+2log_{10}(y)