Question

Consider two quantities u and v that are related by the expression vp=cuq, where c is a constant. the exponents p and q are not necessarily integers. define x=logu and y=logv. find an expression for y in terms of x.

Answer 1

Answer:

y = (q/p)x +log(c)/p

Step-by-step explanation:

$v^{p}=cu^{q}\qquad\text{original equation}\\\\p\log{(v)}=\log{(c)}+q\log{(u)}\qquad\text{take the log}\\\\py=log{(c)}+qx\qquad\text{substitute x and y}\\\\y=\dfrac{\log{(c)}+qx}{p}$