What is 2/3 log_{a}(-2log_{b}(-1/5 log_{c}(x))) ?

The solution to 2/3 log_{a}(-2log_{b}(-1/5 log_{c}(x))) is (2log_{a}(-2log_{b}(-1/5 log_{c}(x))))/3

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simplify 2/3 log_{a}(-2log_{b}(-1/5 log_{c}(x)))

simplify

\frac{2}{3} lo g_{a} (- 2 lo g_{b} (- \frac{1}{5} lo g_{c} (x)))

\frac{2 lo g _{a} ( - 2 lo g _{b} ( - \frac{1}{5} lo g _{c} ( x ) ) )}{3}

Solution steps

\frac{2}{3} lo g_{a} (- 2 lo g_{b} (- \frac{1}{5} lo g_{c} (x)))

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 lo g _{a} ( - 2 lo g _{b} ( - \frac{1}{5} lo g _{c} ( x ) ) )}{3}

ln (2) - ln (10)

lo g_{10} (\frac{5}{x})

lo g_{2} ((x + y) \cdot z)

ln (x^{2} - 9) - ln (x + 3)

lo g_{a} (x) - \frac{1}{2} lo g_{a} (z)

What is 2/3 log_{a}(-2log_{b}(-1/5 log_{c}(x))) ?
The solution to 2/3 log_{a}(-2log_{b}(-1/5 log_{c}(x))) is (2log_{a}(-2log_{b}(-1/5 log_{c}(x))))/3