What is log_{10}((x^2-1)/(sqrt(y)z^3)) ?

The solution to log_{10}((x^2-1)/(sqrt(y)z^3)) is log_{10}(x^2-1)-log_{10}(sqrt(y))-3log_{10}(z)

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simplify log_{10}((x^2-1)/(sqrt(y)z^3))

simplify

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

lo g_{10} (x^{2} - 1) - lo g_{10} (y) - 3 lo g_{10} (z)

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{x ^{2} - 1}{y z ^{3}}) = lo g_{10} (x^{2} - 1) - lo g_{10} (y z^{3})

= lo g_{10} (x^{2} - 1) - lo g_{10} (y z^{3})

Simplify

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

= lo g_{10} (x^{2} - 1) - (lo g_{10} (y) + 3 lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

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

= lo g_{10} (x^{2} - 1) - lo g_{10} (y) - 3 lo g_{10} (z)

4 \cdot lo g_{0.1} (3) - \frac{2}{3} \cdot lo g_{0.1} (27) + 2 \cdot lo g_{0.1} (6)

2 lo g_{2} (7) + lo g_{2} (3)

ln (\frac{1}{8}) - ln (\frac{1}{2})

ln (\frac{x}{7})

ln (\frac{0.4}{0.6})

What is log_{10}((x^2-1)/(sqrt(y)z^3)) ?
The solution to log_{10}((x^2-1)/(sqrt(y)z^3)) is log_{10}(x^2-1)-log_{10}(sqrt(y))-3log_{10}(z)