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

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

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

simplify

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

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

Solution steps

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

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

ln (e^{x^{2}} cos (5 x - 7))

lo g_{3} (8) + lo g_{3} (x) - 2 lo g_{3} (x + 4)

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

ln (\frac{11}{3})

ln (\frac{e}{a})

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