What is log_{10}(a^2)+log_{10}(b)-log_{10}(a) ?

The solution to log_{10}(a^2)+log_{10}(b)-log_{10}(a) is log_{10}(ab)

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simplify log_{10}(a^2)+log_{10}(b)-log_{10}(a)

simplify

lo g_{10} (a^{2}) + lo g_{10} (b) - lo g_{10} (a)

lo g_{10} (ab)

Solution steps

lo g_{10} (a^{2}) + lo g_{10} (b) - lo g_{10} (a)

Apply log rule:

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

lo g_{10} (a^{2}) + lo g_{10} (b) = lo g_{10} (a^{2} b)

= lo g_{10} (a^{2} b) - lo g_{10} (a)

Apply log rule:

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

lo g_{10} (a^{2} b) - lo g_{10} (a) = lo g_{10} (\frac{a ^{2} b}{a})

= lo g_{10} (\frac{a ^{2} b}{a})

Cancel the common factor:

a

= lo g_{10} (ab)

ln (7 x (cos (x))^{\frac{x}{2}})

lo g_{10} (a + b) - lo g_{10} (a) - lo g_{10} (b)

lo g_{10} (\frac{k}{r})

4 lo g_{10} (a) - \frac{1}{2} lo g_{10} (b) + lo g_{10} (c)

ln (e^{19} x^{20})

What is log_{10}(a^2)+log_{10}(b)-log_{10}(a) ?
The solution to log_{10}(a^2)+log_{10}(b)-log_{10}(a) is log_{10}(ab)