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Popular >

simplify log_{2}(9^5)

Solution

simplify

lo g_{2} (9^{5})

Solution

10 lo g_{2} (3)

+1

Decimal Notation

15.84962 \dots

Solution steps

lo g_{2} (9^{5})

Apply log rule:

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

lo g_{2} (9^{5}) = 5 lo g_{2} (9)

= 5 lo g_{2} (9)

Factor the number:

9 = 3^{2}

= 5 lo g_{2} (3^{2})

Apply log rule:

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

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

= 5 \cdot 2 lo g_{2} (3)

Multiply the numbers:

5 \cdot 2 = 10

= 10 lo g_{2} (3)

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Frequently Asked Questions (FAQ)

What is log_{2}(9^5) ?
The solution to log_{2}(9^5) is 10log_{2}(3)