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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (\frac{y}{z ^{9}})

2 x (ln (x) + ln (2)) - 2 x + e

ln (a t e^{c t})

0.5 lo g_{10} (x) + 0.5 lo g_{10} (y)

lo g_{a} (\frac{1}{25})

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