What is log_{10}(m^n)-log_{10}(p^q) ?

The solution to log_{10}(m^n)-log_{10}(p^q) is log_{10}((m^n)/(p^q))

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simplify log_{10}(m^n)-log_{10}(p^q)

simplify

lo g_{10} (m^{n}) - lo g_{10} (p^{q})

lo g_{10} (\frac{m ^{n}}{p ^{q}})

Solution steps

lo g_{10} (m^{n}) - lo g_{10} (p^{q})

Apply log rule:

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

lo g_{10} (m^{n}) - lo g_{10} (p^{q}) = lo g_{10} (\frac{m ^{n}}{p ^{q}})

= lo g_{10} (\frac{m ^{n}}{p ^{q}})

- 3 lo g_{5} (\frac{1}{x}) + \frac{1}{2} lo g_{5} (x)

\frac{1}{2} lo g_{7} (x) - lo g_{7} (x + 1)

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

ln (2 b \frac{b + 1}{b - 1})

ln (\frac{2 x}{x + 3})

What is log_{10}(m^n)-log_{10}(p^q) ?
The solution to log_{10}(m^n)-log_{10}(p^q) is log_{10}((m^n)/(p^q))