What is simplify-log_{2}(1/1000) ?

The solution to simplify-log_{2}(1/1000) is 3log_{2}(10)

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simplify-log_{2}(1/1000)

simplify

- lo g_{2} (\frac{1}{1000})

3 lo g_{2} (10)

Decimal Notation

9.96578 \dots

Solution steps

- lo g_{2} (\frac{1}{1000})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{2} (\frac{1}{1000}) = lo g_{2} (1) - lo g_{2} (1000)

= - (lo g_{2} (1) - lo g_{2} (1000))

Apply log rule:

lo g_{a} (1) = 0

= - (- lo g_{2} (1000) + 0)

0 - lo g_{2} (1000) = - lo g_{2} (1000)

= - (- lo g_{2} (1000))

Apply rule

- (- a) = a

= lo g_{2} (1000)

Rewrite

1000

in power-base form:

1000 = 1 0^{3}

= lo g_{2} (1 0^{3})

Apply log rule:

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

lo g_{2} (1 0^{3}) = 3 lo g_{2} (10)

= 3 lo g_{2} (10)

5 lo g_{2} (x) + 10 lo g_{2} (y)

- lo g_{10} (1.11 \cdot 1 0^{- 10})

ln ∣ 5 + 3 ∣ + 70 e^{3} (3) + 80 - ln (5)

lo g_{4} (\frac{1}{16 x ^{2} z ^{3}})

lo g_{a} (12 x^{3} y)

What is simplify-log_{2}(1/1000) ?
The solution to simplify-log_{2}(1/1000) is 3log_{2}(10)