What is 1/3 log_{c}(x)+5log_{c}(y)-4log_{c}(x) ?

The solution to 1/3 log_{c}(x)+5log_{c}(y)-4log_{c}(x) is 5log_{c}(y)-11/3 log_{c}(x)

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simplify 1/3 log_{c}(x)+5log_{c}(y)-4log_{c}(x)

simplify

\frac{1}{3} lo g_{c} (x) + 5 lo g_{c} (y) - 4 lo g_{c} (x)

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

Solution steps

\frac{1}{3} lo g_{c} (x) + 5 lo g_{c} (y) - 4 lo g_{c} (x)

Group like terms

= 5 lo g_{c} (y) - 4 lo g_{c} (x) + \frac{1}{3} lo g_{c} (x)

Factor out common term

lo g_{c} (x)

= 5 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}

= 5 lo g_{c} (y) - lo g_{c} (x) \frac{11}{3}

= 5 lo g_{c} (y) - \frac{11}{3} lo g_{c} (x)

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

ln (\frac{6 x ^{2}}{y ^{4}})

lo g_{10} (lo g_{10} (1000 0^{25 x}))

ln (3 x + 1) - ln (x + 2)

lo g_{3} (\frac{ab}{c d})

What is 1/3 log_{c}(x)+5log_{c}(y)-4log_{c}(x) ?
The solution to 1/3 log_{c}(x)+5log_{c}(y)-4log_{c}(x) is 5log_{c}(y)-11/3 log_{c}(x)