What is expand log_{10}((xz^2)/y) ?

The solution to expand log_{10}((xz^2)/y) is log_{10}(x)+2log_{10}(z)-log_{10}(y)

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expand log_{10}((xz^2)/y)

expand

lo g_{10} (\frac{x z ^{2}}{y})

lo g_{10} (x) + 2 lo g_{10} (z) - lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x z ^{2}}{y})

Apply log rule:

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

lo g_{10} (\frac{x z ^{2}}{y}) = lo g_{10} (x z^{2}) - lo g_{10} (y)

= lo g_{10} (x z^{2}) - lo g_{10} (y)

Apply log rule:

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

lo g_{10} (x z^{2}) = lo g_{10} (x) + lo g_{10} (z^{2})

= lo g_{10} (x) + lo g_{10} (z^{2}) - lo g_{10} (y)

Apply log rule:

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

lo g_{10} (z^{2}) = 2 lo g_{10} (z)

= lo g_{10} (x) + 2 lo g_{10} (z) - lo g_{10} (y)

ln (x + 3) - ln (4)

2 ln (10) - ln (5) - 2 ln (2) + ln (3)

- lo g_{10} (8.41 \cdot 0.001)

ln (\frac{0.5}{1.5})

ln (\frac{9 - 3 x ^{2}}{x})

What is expand log_{10}((xz^2)/y) ?
The solution to expand log_{10}((xz^2)/y) is log_{10}(x)+2log_{10}(z)-log_{10}(y)