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

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

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

simplify

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

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

Solution steps

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

Apply log rule:

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

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

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

Cancel the common factor:

y

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

lo g_{10} (\frac{m ^{2} + n}{1000})

ln (10) - ln (6)

ln (10) - ln (8)

2 - \frac{1}{2} lo g_{n} (4) - lo g_{n} (5)

2 ln (5) + \frac{7}{5} - 2 ln (- 3) - \frac{7}{3}

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