Question

If u = In5 and v = in2, write in 8/25 in terms of u and v

Answer 1

Answer:

$\frac{8}{25} = {e}^{3v - 2u}$

Step-by-step explanation:

If

$u = \ln(5) \: then \: 5 = {e}^{u}$

If

$v= \ln(2) \: then \: 2= {e}^{v}$

We want to write 8/25 in terms of u and v.

We use properties of exponents to get:

$\frac{8}{25} = \frac{ {2}^{3} }{ {5}^{2} }$

We substitute for 5 and 2 to obtain:

$\frac{8}{25} = \frac{( { {e}^{v}) }^{3} }{ ({ {e}^{u}) }^{2} }$

This simplifies to:

$\frac{8}{25} = \frac{{ {e}^{3v}}}{ { {e}^{2u} } }$

This gives us

$\frac{8}{25} = {e}^{3v - 2u}$