What is 8log_{10}(x)-2log_{10}(y) ?

The solution to 8log_{10}(x)-2log_{10}(y) is log_{10}((x^8)/(y^2))

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simplify 8log_{10}(x)-2log_{10}(y)

simplify

8 lo g_{10} (x) - 2 lo g_{10} (y)

lo g_{10} (\frac{x ^{8}}{y ^{2}})

Solution steps

8 lo g_{10} (x) - 2 lo g_{10} (y)

Apply log rule:

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

8 lo g_{10} (x) = lo g_{10} (x^{8})

= lo g_{10} (x^{8}) - 2 lo g_{10} (y)

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} (x^{8}) - lo g_{10} (y^{2})

Apply log rule:

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

lo g_{10} (x^{8}) - lo g_{10} (y^{2}) = lo g_{10} (\frac{x ^{8}}{y ^{2}})

= lo g_{10} (\frac{x ^{8}}{y ^{2}})

ln (\frac{8}{8 + 1})

ln (x) + ln (3)

3 ln (2 - x) + 3 ln (2 + x)

- lo g_{10} (6.7 \cdot 1 0^{- 5})

- lo g_{10} (8.5 \cdot 1 0^{- 1})

What is 8log_{10}(x)-2log_{10}(y) ?
The solution to 8log_{10}(x)-2log_{10}(y) is log_{10}((x^8)/(y^2))