What is log_{10}((x^3)/(y^4)) ?

The solution to log_{10}((x^3)/(y^4)) is 3log_{10}(x)-4log_{10}(y)

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simplify log_{10}((x^3)/(y^4))

simplify

lo g_{10} (\frac{x ^{3}}{y ^{4}})

3 lo g_{10} (x) - 4 lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x ^{3}}{y ^{4}})

Apply log rule:

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

lo g_{10} (\frac{x ^{3}}{y ^{4}}) = lo g_{10} (x^{3}) - lo g_{10} (y^{4})

= lo g_{10} (x^{3}) - lo g_{10} (y^{4})

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

lo g_{10} (y^{4}) = 4 lo g_{10} (y)

= 3 lo g_{10} (x) - 4 lo g_{10} (y)

lo g_{10} (x) + 5 lo g_{10} (y) - 4 lo g_{10} (z)

2 ln (x) - \frac{1}{2} ln (y)

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

lo g_{3} (7) + \frac{1}{2} lo g_{3} (t) - lo g_{3} (r)

\frac{1}{2} \cdot ln (2)

What is log_{10}((x^3)/(y^4)) ?
The solution to log_{10}((x^3)/(y^4)) is 3log_{10}(x)-4log_{10}(y)