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Popular >

simplify log_{3}(8^3*9^8)

Solution

simplify

lo g_{3} (8^{3} \cdot 9^{8})

Solution

9 lo g_{3} (2) + 16

+1

Decimal Notation

21.67836 \dots

Solution steps

lo g_{3} (8^{3} \cdot 9^{8})

9^{8} = 3^{16}

= lo g_{3} (8^{3} \cdot 3^{16})

Apply log rule:

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

lo g_{3} (8^{3} \cdot 3^{16}) = lo g_{3} (8^{3}) + lo g_{3} (3^{16})

= lo g_{3} (8^{3}) + lo g_{3} (3^{16})

lo g_{3} (8^{3}) = 9 lo g_{3} (2)

= 9 lo g_{3} (2) + lo g_{3} (3^{16})

Apply log rule:

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

lo g_{3} (3^{16}) = 16

= 9 lo g_{3} (2) + 16

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Frequently Asked Questions (FAQ)

What is log_{3}(8^3*9^8) ?
The solution to log_{3}(8^3*9^8) is 9log_{3}(2)+16