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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

Simplify

lo g_{10} (y^{3} z^{2}) : 3 lo g_{10} (y) + 2 lo g_{10} (z)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

lo g_{10} (\frac{x ^{17} y ^{2}}{z ^{16}})

5 ln (x + y) - 2 ln (y) - 8 ln (x)

2 lo g_{a} (x^{4}) + 4 lo g_{a} ((2 x)^{2})

4 ln (x) - \frac{1}{7} ln (y)

lo g_{10} (\frac{x ^{3} ( x + 1 )}{( x - 2 ) ^{2}})

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