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

Answer:

$\ln( \frac{8}{25} ) = 3v - 2u$

Step-by-step 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

$\ln( \frac{8}{25} )$

Which is

$\ln( \frac{8}{25} ) = ln(8) - ln(25)$

$\ln( \frac{8}{25} ) = ln( {2}^{3} ) - ln( {5}^{2} )$

$\ln( \frac{8}{25} ) = 3 ln( {2} ) - 2ln(5)$

$\ln( \frac{8}{25} ) = 3v - 2u$