What is simplify-log_{0.5}(2x)-3 ?

The solution to simplify-log_{0.5}(2x)-3 is log_{2}(x)-2

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simplify-log_{0.5}(2x)-3

simplify

- lo g_{0.5} (2 x) - 3

lo g_{2} (x) - 2

Solution steps

- lo g_{0.5} (2 x) - 3

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{0.5} (2 x) = lo g_{0.5} (2) + lo g_{0.5} (x)

= - (lo g_{0.5} (x) + lo g_{0.5} (2)) - 3

- (lo g_{0.5} (2) + lo g_{0.5} (x)) = - (- 1 - lo g_{2} (x))

= - (- lo g_{2} (x) - 1) - 3

- (- 1 - lo g_{2} (x)) : 1 + lo g_{2} (x)

= 1 + lo g_{2} (x) - 3

Simplify

1 + lo g_{2} (x) - 3 : lo g_{2} (x) - 2

= lo g_{2} (x) - 2

ln (\frac{e ^{(x + 2)} ( 5 x + 1 ) ^{3}}{x ^{5} ( 2 x + 1 ) ^{7}})

\frac{19.16}{0.004 \cdot 0.02} ln (\frac{1}{1 - 0.9})

ln (\frac{e ^{3} y ^{2}}{x})

0.4 lo g_{2} (0.4) + 0.6 lo g_{2} (0.6)

4 \cdot ln (\frac{1}{2})

What is simplify-log_{0.5}(2x)-3 ?
The solution to simplify-log_{0.5}(2x)-3 is log_{2}(x)-2