What is 2log_{1000}(-3log_{0.01}(x)) ?

The solution to 2log_{1000}(-3log_{0.01}(x)) is 2log_{1000}(3)+2log_{1000}(-log_{100}(x))

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simplify 2log_{1000}(-3log_{0.01}(x))

simplify

2 lo g_{1000} (- 3 lo g_{0.01} (x))

2 lo g_{1000} (3) + 2 lo g_{1000} (- lo g_{100} (x))

Solution steps

2 lo g_{1000} (- 3 lo g_{0.01} (x))

Apply log rule:

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

2 lo g_{1000} (- 3 lo g_{0.01} (x)) = 2 lo g_{1000} (3) + 2 lo g_{1000} (lo g_{0.01} (x))

= 2 lo g_{1000} (3) + 2 lo g_{1000} (lo g_{0.01} (x))

Simplify

lo g_{0.01} (x) : - lo g_{100} (x)

= 2 lo g_{1000} (3) + 2 lo g_{1000} (- lo g_{100} (x))

- 10 ln (\frac{0.0001}{0.04})

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lo g_{a} (3) + 2 lo g_{a} (x)

What is 2log_{1000}(-3log_{0.01}(x)) ?
The solution to 2log_{1000}(-3log_{0.01}(x)) is 2log_{1000}(3)+2log_{1000}(-log_{100}(x))