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Popular >

simplify log_{3}(81x^2)

Solution

simplify

lo g_{3} (81 x^{2})

Solution

4 + 2 lo g_{3} (x)

Solution steps

lo g_{3} (81 x^{2})

Factor the number:

81 = 3^{4}

= lo g_{3} (3^{4} x^{2})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{3} (3^{4} x^{2}) = lo g_{3} (3^{4}) + lo g_{3} (x^{2})

= lo g_{3} (3^{4}) + lo g_{3} (x^{2})

Apply log rule:

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

lo g_{3} (3^{4}) = 4

= 4 + lo g_{3} (x^{2})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{3} (x^{2}) = 2 lo g_{3} (x)

= 4 + 2 lo g_{3} (x)

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Frequently Asked Questions (FAQ)

What is log_{3}(81x^2) ?
The solution to log_{3}(81x^2) is 4+2log_{3}(x)