What is 3log_{2}(p)+5log_{2}(q) ?

The solution to 3log_{2}(p)+5log_{2}(q) is log_{2}(p^3q^5)

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simplify 3log_{2}(p)+5log_{2}(q)

simplify

3 lo g_{2} (p) + 5 lo g_{2} (q)

lo g_{2} (p^{3} q^{5})

Solution steps

3 lo g_{2} (p) + 5 lo g_{2} (q)

Apply log rule:

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

3 lo g_{2} (p) = lo g_{2} (p^{3})

= lo g_{2} (p^{3}) + 5 lo g_{2} (q)

Apply log rule:

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

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

= lo g_{2} (p^{3}) + lo g_{2} (q^{5})

Apply log rule:

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

lo g_{2} (p^{3}) + lo g_{2} (q^{5}) = lo g_{2} (p^{3} q^{5})

= lo g_{2} (p^{3} q^{5})

lo g_{10} (\frac{( x - 6 ) ^{2}}{( 2 x ) ^{3}})

\frac{1}{2} ln (\frac{1 + 0.919}{1 - 0.919})

ln ((x^{5} y)^{5})

2 ln (3) - ln (18)

lo g_{b} (y z^{2})

What is 3log_{2}(p)+5log_{2}(q) ?
The solution to 3log_{2}(p)+5log_{2}(q) is log_{2}(p^3q^5)