What is 5log_{2}(c)+1/3 log_{2}(d) ?

The solution to 5log_{2}(c)+1/3 log_{2}(d) is log_{2}(c^5d^{1/3})

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simplify 5log_{2}(c)+1/3 log_{2}(d)

simplify

5 lo g_{2} (c) + \frac{1}{3} lo g_{2} (d)

lo g_{2} (c^{5} d^{\frac{1}{3}})

Solution steps

5 lo g_{2} (c) + \frac{1}{3} lo g_{2} (d)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 lo g_{2} (c) = lo g_{2} (c^{5})

= lo g_{2} (c^{5}) + \frac{1}{3} lo g_{2} (d)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{3} lo g_{2} (d) = lo g_{2} (d^{\frac{1}{3}})

= lo g_{2} (c^{5}) + lo g_{2} (d^{\frac{1}{3}})

Apply log rule:

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

lo g_{2} (c^{5}) + lo g_{2} (d^{\frac{1}{3}}) = lo g_{2} (c^{5} d^{\frac{1}{3}})

= lo g_{2} (c^{5} d^{\frac{1}{3}})

ln (\frac{r ^{2} s ^{11}}{t ^{14}})

ln (a h^{m})

- \frac{1}{10} lo g_{2} (\frac{1}{10}) - \frac{9}{10} lo g_{2} (\frac{9}{10})

3 lo g_{b} (y) - \frac{19}{4} lo g_{b} (x)

15 ln (\frac{3 ln ( 11 )}{2}) - 4

What is 5log_{2}(c)+1/3 log_{2}(d) ?
The solution to 5log_{2}(c)+1/3 log_{2}(d) is log_{2}(c^5d^{1/3})