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Popular >

simplify log_{10}(9)(3)

Solution

simplify

lo g_{10} (9) (3)

Solution

6 lo g_{10} (3)

+1

Decimal Notation

2.86272 \dots

Solution steps

lo g_{10} (9) (3)

Apply rule:

(a) = a

(3) = 3

= lo g_{10} (9) \cdot 3

Factor the number:

9 = 3^{2}

= lo g_{10} (3^{2}) \cdot 3

Apply log rule:

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

lo g_{10} (3^{2}) = 2 lo g_{10} (3)

= 2 lo g_{10} (3) \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6 lo g_{10} (3)

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Frequently Asked Questions (FAQ)

What is log_{10}(9)(3) ?
The solution to log_{10}(9)(3) is 6log_{10}(3)