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

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

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

expand

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

4 lo g_{10} (z) - 5 lo g_{10} (x) - lo g_{10} (y)

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{z ^{4}}{x ^{5} y}) = lo g_{10} (z^{4}) - lo g_{10} (x^{5} y)

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

Apply log rule:

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

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

= 4 lo g_{10} (z) - 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)

= 4 lo g_{10} (z) - (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)

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

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

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

ln (x) + ln (x^{2} + 1)

ln (6 H)

- lo g_{10} (1.87 \cdot 1 0^{- 9})

8.314 \cdot ln (3.95 \cdot 1 0^{9})

ln (\frac{5918}{87})

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