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Popular >

simplify log_{3}(27a)-log_{3}(a)

Solution

simplify

lo g_{3} (27 a) - lo g_{3} (a)

Solution

3

Solution steps

lo g_{3} (27 a) - lo g_{3} (a)

Apply log rule:

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

lo g_{3} (27 a) - lo g_{3} (a) = lo g_{3} (\frac{27 a}{a})

= lo g_{3} (\frac{27 a}{a})

Simplify

\frac{27 a}{a} : 27

= lo g_{3} (27)

Factor the number:

27 = 3^{3}

= lo g_{3} (3^{3})

Apply log rule:

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

= 3

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Frequently Asked Questions (FAQ)

What is log_{3}(27a)-log_{3}(a) ?
The solution to log_{3}(27a)-log_{3}(a) is 3