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Popular >

simplify log_{3}(9^2*7^4)

Solution

simplify

lo g_{3} (9^{2} \cdot 7^{4})

Solution

4 + 4 lo g_{3} (7)

+1

Decimal Notation

11.08497 \dots

Solution steps

lo g_{3} (9^{2} \cdot 7^{4})

9^{2} = 3^{4}

= lo g_{3} (3^{4} \cdot 7^{4})

Apply log rule:

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

lo g_{3} (3^{4} \cdot 7^{4}) = lo g_{3} (3^{4}) + lo g_{3} (7^{4})

= lo g_{3} (3^{4}) + lo g_{3} (7^{4})

Apply log rule:

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

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

= 4 + lo g_{3} (7^{4})

Apply log rule:

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

lo g_{3} (7^{4}) = 4 lo g_{3} (7)

= 4 + 4 lo g_{3} (7)

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Frequently Asked Questions (FAQ)

What is log_{3}(9^2*7^4) ?
The solution to log_{3}(9^2*7^4) is 4+4log_{3}(7)