What is expand log_{2}((p^3sqrt(q))/(16r^2)) ?

The solution to expand log_{2}((p^3sqrt(q))/(16r^2)) is 3log_{2}(p)+log_{2}(sqrt(q))-4-2log_{2}(r)

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expand log_{2}((p^3sqrt(q))/(16r^2))

expand

lo g_{2} (\frac{p ^{3} q}{16 r ^{2}})

3 lo g_{2} (p) + lo g_{2} (q) - 4 - 2 lo g_{2} (r)

Solution steps

lo g_{2} (\frac{p ^{3} q}{16 r ^{2}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{2} (\frac{p ^{3} q}{16 r ^{2}}) = lo g_{2} (p^{3} q) - lo g_{2} (16 r^{2})

= lo g_{2} (p^{3} q) - lo g_{2} (16 r^{2})

Apply log rule:

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

lo g_{2} (p^{3} q) = lo g_{2} (p^{3}) + lo g_{2} (q), lo g_{2} (16 r^{2}) = lo g_{2} (16) + lo g_{2} (r^{2})

= lo g_{2} (p^{3}) + lo g_{2} (q) - (lo g_{2} (r^{2}) + lo g_{2} (16))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 3 lo g_{2} (p) + lo g_{2} (q) - (lo g_{2} (16) + lo g_{2} (r^{2}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{2} (r^{2}) = 2 lo g_{2} (r)

= 3 lo g_{2} (p) + lo g_{2} (q) - (lo g_{2} (16) + 2 lo g_{2} (r))

lo g_{2} (16) = 4

= 3 lo g_{2} (p) + lo g_{2} (q) - (2 lo g_{2} (r) + 4)

- (4 + 2 lo g_{2} (r)) : - 4 - 2 lo g_{2} (r)

= 3 lo g_{2} (p) + lo g_{2} (q) - 4 - 2 lo g_{2} (r)

\frac{1}{3} ln (\frac{65}{76})

3 ln (x) + 4 ln (yz) - ln (x^{2} y^{2})

3 ln (3) - 4 ln (2) + 1

ln (x^{12} \frac{y ^{19}}{z ^{2}})

4 ln^{3} (- 6 e^{3} + \frac{9}{2})

What is expand log_{2}((p^3sqrt(q))/(16r^2)) ?
The solution to expand log_{2}((p^3sqrt(q))/(16r^2)) is 3log_{2}(p)+log_{2}(sqrt(q))-4-2log_{2}(r)