What is expand log_{10}(5x^4y) ?

The solution to expand log_{10}(5x^4y) is log_{10}(5)+4log_{10}(x)+log_{10}(y)

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expand log_{10}(5x^4y)

expand

lo g_{10} (5 x^{4} y)

lo g_{10} (5) + 4 lo g_{10} (x) + lo g_{10} (y)

Solution steps

lo g_{10} (5 x^{4} y)

Apply log rule:

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

lo g_{10} (5 x^{4} y) = lo g_{10} (5) + lo g_{10} (x^{4}) + lo g_{10} (y)

= lo g_{10} (5) + lo g_{10} (x^{4}) + lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x^{4}) = 4 lo g_{10} (x)

= lo g_{10} (5) + 4 lo g_{10} (x) + lo g_{10} (y)

ln (\frac{( x + 1 ) ( x - 10 )}{( x - 1 ) ( x + 10 )})

\frac{1}{3} lo g_{3} (5 x)

3 lo g_{10} (a) + lo g_{10} (b) - lo g_{10} (c)

ln (\frac{7 + 41}{4})

What is expand log_{10}(5x^4y) ?
The solution to expand log_{10}(5x^4y) is log_{10}(5)+4log_{10}(x)+log_{10}(y)