What is simplify-log_{2}(1/36) ?

The solution to simplify-log_{2}(1/36) is 2log_{2}(6)

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simplify-log_{2}(1/36)

simplify

- lo g_{2} (\frac{1}{36})

2 lo g_{2} (6)

Decimal Notation

5.16992 \dots

Solution steps

- lo g_{2} (\frac{1}{36})

Apply log rule:

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

lo g_{2} (\frac{1}{36}) = lo g_{2} (1) - lo g_{2} (36)

= - (lo g_{2} (1) - lo g_{2} (36))

Apply log rule:

lo g_{a} (1) = 0

= - (- lo g_{2} (36) + 0)

0 - lo g_{2} (36) = - lo g_{2} (36)

= - (- lo g_{2} (36))

Apply rule

- (- a) = a

= lo g_{2} (36)

Rewrite

36

in power-base form:

36 = 6^{2}

= lo g_{2} (6^{2})

Apply log rule:

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

lo g_{2} (6^{2}) = 2 lo g_{2} (6)

= 2 lo g_{2} (6)

ln (x^{2}) + ln (x)

\frac{2}{3} ln (5 (2))

ln (- 2 i)

ln (\frac{y}{x}) + ln (\frac{1}{x + y}) - ln (\frac{x}{6})

- lo g_{10} (4.6 \cdot 1 0^{- 3})

What is simplify-log_{2}(1/36) ?
The solution to simplify-log_{2}(1/36) is 2log_{2}(6)