What is log_{x}(-2log_{y}(+log_{z}(x))) ?

The solution to log_{x}(-2log_{y}(+log_{z}(x))) is log_{x}(2)+log_{x}(log_{y}(log_{z}(x)))

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simplify log_{x}(-2log_{y}(+log_{z}(x)))

simplify

lo g_{x} (- 2 lo g_{y} (+ lo g_{z} (x)))

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

Solution steps

lo g_{x} (- 2 lo g_{y} (lo g_{z} (x)))

Apply log rule:

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

lo g_{x} (- 2 lo g_{y} (lo g_{z} (x))) = lo g_{x} (2) + lo g_{x} (lo g_{y} (lo g_{z} (x)))

= lo g_{x} (2) + lo g_{x} (lo g_{y} (lo g_{z} (x)))

\frac{6 ln ( 7 ) - 2 ln ( 5 )}{- ln ( 5 ) - 5 ln ( 7 )}

20 \cdot lo g_{10} (\frac{4 π \cdot 2}{644334})

\frac{4}{3} lo g_{3} (2)

lo g_{2} (\frac{6 ^{4}}{1 1 ^{6}})

ln (20) - ln (3)

What is log_{x}(-2log_{y}(+log_{z}(x))) ?
The solution to log_{x}(-2log_{y}(+log_{z}(x))) is log_{x}(2)+log_{x}(log_{y}(log_{z}(x)))