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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{ln ( 5.9 ) - ln ( 6 )}{5.9 - 6}

ln (\frac{x ^{2}}{y})

ln (\frac{e ^{2 y}}{c})

4 lo g_{a} (k) - 3 lo g_{a} (m)

- lo g_{10} (8.32 \cdot 1 0^{- 9})

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