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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (e^{x} + 1) - ln (e^{- x} + 1)

ln (x) - ln (x^{2} + 4)

- lo g_{10} (4 \cdot 1 0^{- 7})

ln (\frac{e ^{2} - e ^{4} - 1}{2 - 5})

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