Question

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

Answer 1

`(8)/(25) = {e}^(3v - 2u)`

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:

`(8)/(25) = \frac{ {2}^(3) }{ {5}^(2) }`

We substitute for 5 and 2 to obtain:

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

This simplifies to:

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

This gives us

`(8)/(25) = {e}^(3v - 2u)`