What is simplify-log_{2}(1/100) ?

The solution to simplify-log_{2}(1/100) is 2log_{2}(10)

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simplify-log_{2}(1/100)

simplify

- lo g_{2} (\frac{1}{100})

2 lo g_{2} (10)

Decimal Notation

6.64385 \dots

Solution steps

- lo g_{2} (\frac{1}{100})

Apply log rule:

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

lo g_{2} (\frac{1}{100}) = lo g_{2} (1) - lo g_{2} (100)

= - (lo g_{2} (1) - lo g_{2} (100))

Apply log rule:

lo g_{a} (1) = 0

= - (- lo g_{2} (100) + 0)

0 - lo g_{2} (100) = - lo g_{2} (100)

= - (- lo g_{2} (100))

Apply rule

- (- a) = a

= lo g_{2} (100)

Rewrite

100

in power-base form:

100 = 1 0^{2}

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

Apply log rule:

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

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

= 2 lo g_{2} (10)

ln (y θ^{(k + 1)} \cdot x)

ln (a (2 x + 1) e^{- a x (x + 1)})

\frac{2 ln ( 2 )}{ln ( 5 )} - 4

lo g_{10} (y^{5} x)

ln (- sin (x) + 1) - ln (sin (x) + 1)

What is simplify-log_{2}(1/100) ?
The solution to simplify-log_{2}(1/100) is 2log_{2}(10)