What is expand log_{10}((x^3y^2)/z) ?

The solution to expand log_{10}((x^3y^2)/z) is 3log_{10}(x)+2log_{10}(y)-log_{10}(z)

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expand log_{10}((x^3y^2)/z)

expand

lo g_{10} (\frac{x ^{3} y ^{2}}{z})

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

Solution steps

lo g_{10} (\frac{x ^{3} y ^{2}}{z})

Apply log rule:

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

lo g_{10} (\frac{x ^{3} y ^{2}}{z}) = lo g_{10} (x^{3} y^{2}) - lo g_{10} (z)

= lo g_{10} (x^{3} y^{2}) - lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{3} y^{2}) = lo g_{10} (x^{3}) + lo g_{10} (y^{2})

= lo g_{10} (x^{3}) + lo g_{10} (y^{2}) - lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= 3 lo g_{10} (x) + lo g_{10} (y^{2}) - lo g_{10} (z)

Apply log rule:

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

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

= 3 lo g_{10} (x) + 2 lo g_{10} (y) - lo g_{10} (z)

lo g_{3} (13 x)

- lo g_{10} (4 x)

- 2 [ln (2 x) - ln (3)]

\frac{5 ln ( 2 )}{ln ( \frac{5}{4} )}

lo g_{10} (an t i lo g_{4} (lo g_{2} (20) - 1))

What is expand log_{10}((x^3y^2)/z) ?
The solution to expand log_{10}((x^3y^2)/z) is 3log_{10}(x)+2log_{10}(y)-log_{10}(z)