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

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

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expand log_{10}(x^5y)

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (x^{5}) = 5 lo g_{10} (x)

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

ln (\frac{- x}{x ^{2} - 3})

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

\frac{7}{2} ln ∣ 2 (0.5 - 3) ∣ - \frac{7}{2} ln ∣ 2 (- 0.5 - 3) ∣

3 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 7)

- \frac{3}{4} lo g_{e} (\frac{3}{4}) - \frac{1}{4} lo g_{e} (\frac{1}{4})

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