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Popular >

simplify log_{2}(10000000)

Solution

simplify

lo g_{2} (10000000)

Solution

7 + 7 lo g_{2} (5)

+1

Decimal Notation

23.25349 \dots

Solution steps

lo g_{2} (10000000)

Factor the number:

10000000 = 2^{7} \cdot 78125

= lo g_{2} (2^{7} \cdot 78125)

Apply log rule:

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

lo g_{2} (2^{7} \cdot 78125) = lo g_{2} (2^{7}) + lo g_{2} (78125)

= lo g_{2} (2^{7}) + lo g_{2} (78125)

Apply log rule:

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

lo g_{2} (2^{7}) = 7

= 7 + lo g_{2} (78125)

lo g_{2} (78125) = 7 lo g_{2} (5)

= 7 + 7 lo g_{2} (5)

Popular Examples

simplify log_{100}(sqrt(10))simplify

lo g_{100} (10)

simplify (12.5)/(sqrt(16))simplify

\frac{12.5}{16}

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\frac{5}{3} \times 9

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\frac{14 x ^{8} y ^{6}}{21 x ^{8} y ^{2}}

simplify 5^2(-10)^{-4}simplify

5^{2} (- 10)^{- 4}

Frequently Asked Questions (FAQ)

What is log_{2}(10000000) ?
The solution to log_{2}(10000000) is 7+7log_{2}(5)