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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)

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kudzordzifrancis

Answer:

[tex]\ln( \frac{8}{25} ) = 3v - 2u[/tex]

Step-by-step explanation:

We have that

[tex]u= \ln(5) [/tex]

and

[tex]v = \ln2[/tex]

This implies that;

[tex]5 = {e}^{u} [/tex]

and

[tex]2 = {e}^{v} [/tex]

Now find and expresion for

[tex] \ln( \frac{8}{25} ) [/tex]

Which is

[tex]\ln( \frac{8}{25} ) = ln(8) - ln(25) [/tex]

[tex]\ln( \frac{8}{25} ) = ln( {2}^{3} ) - ln( {5}^{2} ) [/tex]

[tex]\ln( \frac{8}{25} ) = 3 ln( {2} ) - 2ln(5) [/tex]

[tex]\ln( \frac{8}{25} ) = 3v - 2u[/tex]