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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

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

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

ln (\frac{e ^{3}}{10})

ln (x^{5} y^{8})

ln (\frac{x ^{4} y}{3 z ^{5}})

ln (x^{3} 2 - x)

3 lo g_{10} (x) - 6 lo g_{10} (x + 1)

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