What is log_{10}((p^2q^3)/(r^4)) ?

The solution to log_{10}((p^2q^3)/(r^4)) is 2log_{10}(p)+3log_{10}(q)-4log_{10}(r)

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simplify log_{10}((p^2q^3)/(r^4))

simplify

lo g_{10} (\frac{p ^{2} q ^{3}}{r ^{4}})

2 lo g_{10} (p) + 3 lo g_{10} (q) - 4 lo g_{10} (r)

Solution steps

lo g_{10} (\frac{p ^{2} q ^{3}}{r ^{4}})

Apply log rule:

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

lo g_{10} (\frac{p ^{2} q ^{3}}{r ^{4}}) = lo g_{10} (p^{2} q^{3}) - lo g_{10} (r^{4})

= lo g_{10} (p^{2} q^{3}) - lo g_{10} (r^{4})

lo g_{10} (p^{2} q^{3}) = 2 lo g_{10} (p) + 3 lo g_{10} (q)

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

= 2 lo g_{10} (p) + 3 lo g_{10} (q) - 4 lo g_{10} (r)

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

5 a^{4} b^{2} - 5 a^{2} b^{4}

(\frac{4}{5 p - 2})^{3}

(x^{3})^{7}

16 x^{2} - 4 y^{2}

What is log_{10}((p^2q^3)/(r^4)) ?
The solution to log_{10}((p^2q^3)/(r^4)) is 2log_{10}(p)+3log_{10}(q)-4log_{10}(r)