What is simplify-2log_{10}(y)+3log_{10}(x) ?

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

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simplify-2log_{10}(y)+3log_{10}(x)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 lo g_{10} (y) = lo g_{10} (y^{2})

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

- lo g_{10} (1.77 \cdot 1 0^{4})

ln (\frac{x}{15})

ln (4) - (ln (4) - ln (3))

lo g_{1000000} (2 π)

ln (\frac{77}{37})

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