What is 1/3 log_{c}(x)+2log_{c}(y)-4log_{c}(x) ?

The solution to 1/3 log_{c}(x)+2log_{c}(y)-4log_{c}(x) is 2log_{c}(y)-11/3 log_{c}(x)

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simplify 1/3 log_{c}(x)+2log_{c}(y)-4log_{c}(x)

simplify

\frac{1}{3} lo g_{c} (x) + 2 lo g_{c} (y) - 4 lo g_{c} (x)

2 lo g_{c} (y) - \frac{11}{3} lo g_{c} (x)

Solution steps

\frac{1}{3} lo g_{c} (x) + 2 lo g_{c} (y) - 4 lo g_{c} (x)

Group like terms

= 2 lo g_{c} (y) - 4 lo g_{c} (x) + \frac{1}{3} lo g_{c} (x)

Factor out common term

lo g_{c} (x)

= 2 lo g_{c} (y) + lo g_{c} (x) (- 4 + \frac{1}{3})

Simplify

lo g_{c} (x) (- 4 + \frac{1}{3}) : - lo g_{c} (x) \frac{11}{3}

= 2 lo g_{c} (y) - lo g_{c} (x) \frac{11}{3}

= 2 lo g_{c} (y) - \frac{11}{3} lo g_{c} (x)

lo g_{10} (3) + lo g_{10} (6) - lo g_{10} (2)

ln (y^{3}) + \frac{1}{3} ln (x^{3} y^{6}) - 5 ln (y)

lo g_{10} (x) - 3 lo g_{10} (2 y) + 4 lo g_{10} (z)

3 ln (2) + 4 ln (x) - ln (5) - 2 ln (y)

lo g_{10} (\frac{x}{y ^{2}})

What is 1/3 log_{c}(x)+2log_{c}(y)-4log_{c}(x) ?
The solution to 1/3 log_{c}(x)+2log_{c}(y)-4log_{c}(x) is 2log_{c}(y)-11/3 log_{c}(x)