What is 5log_{a}(a)-log_{a}(a^4)+log_{a}(a^{-2}) ?

The solution to 5log_{a}(a)-log_{a}(a^4)+log_{a}(a^{-2}) is 5-log_{a}(a^6)

Popular >

simplify 5log_{a}(a)-log_{a}(a^4)+log_{a}(a^{-2})

simplify

5 lo g_{a} (a) - lo g_{a} (a^{4}) + lo g_{a} (a^{- 2})

5 - lo g_{a} (a^{6})

Solution steps

5 lo g_{a} (a) - lo g_{a} (a^{4}) + lo g_{a} (a^{- 2})

Apply log rule:

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

lo g_{a} (a^{- 2}) - lo g_{a} (a^{4}) = lo g_{a} (\frac{a ^{- 2}}{a ^{4}})

= 5 lo g_{a} (a) + lo g_{a} (\frac{a ^{- 2}}{a ^{4}})

Simplify

\frac{a ^{- 2}}{a ^{4}} : \frac{1}{a ^{6}}

= 5 lo g_{a} (a) + lo g_{a} (\frac{1}{a ^{6}})

5 lo g_{a} (a) = 5

= 5 + lo g_{a} (\frac{1}{a ^{6}})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= 5 - lo g_{a} (a^{6})

lo g_{10} (100 x y)

lo g_{2} (3 x) + 1

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

lo g_{10} (y^{7} x z^{3})

3 ln (x) - \frac{1}{2} ln (3 x + 1) + 5 ln (x - 1) - ln (x + 5)

What is 5log_{a}(a)-log_{a}(a^4)+log_{a}(a^{-2}) ?
The solution to 5log_{a}(a)-log_{a}(a^4)+log_{a}(a^{-2}) is 5-log_{a}(a^6)