What is 5log_{10}(x)-4log_{10}(y) ?

The solution to 5log_{10}(x)-4log_{10}(y) is log_{10}((x^5)/(y^4))

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simplify 5log_{10}(x)-4log_{10}(y)

simplify

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

lo g_{10} (\frac{x ^{5}}{y ^{4}})

Solution steps

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

Apply log rule:

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

5 lo g_{10} (x) = lo g_{10} (x^{5})

= lo g_{10} (x^{5}) - 4 lo g_{10} (y)

Apply log rule:

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

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

= lo g_{10} (x^{5}) - lo g_{10} (y^{4})

Apply log rule:

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

lo g_{10} (x^{5}) - lo g_{10} (y^{4}) = lo g_{10} (\frac{x ^{5}}{y ^{4}})

= lo g_{10} (\frac{x ^{5}}{y ^{4}})

- lo g_{10} (5 (1 0^{- 6}))

ln (\frac{- 0.375}{( - 0.375 ) ^{3} - 8}) + 3

\frac{1}{3} \cdot ln (1 + 2 \cdot 100) + \frac{2}{3} \cdot ln (1 + 2 \cdot 400)

- ln (\frac{131}{441.00049})

[ln (- 1) - ln (- 2)]

What is 5log_{10}(x)-4log_{10}(y) ?
The solution to 5log_{10}(x)-4log_{10}(y) is log_{10}((x^5)/(y^4))