Question

PLEASE HELP. TAKE AT HOME TEST. if u = LN5 and v = LN2, write LN8/15 in terms of u and v. (8/15 is 8 over 25)

Answer 1

`\ln( (8)/(25) ) = 3v - 2u`

Explanation:

We have that

`u= \ln(5)`

and

`v = \ln2`

This implies that;

`5 = {e}^(u)`

and

`2 = {e}^(v)`

Now find and expresion for

`\ln( (8)/(25) )`

Which is

`\ln( (8)/(25) ) = ln(8) - ln(25)`

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

`\ln( (8)/(25) ) = 3 ln( {2} ) - 2ln(5)`

`\ln( (8)/(25) ) = 3v - 2u`