Question

Solve the following equation:
-2/3 ln (k-8) + 2/3 ln (k-1) = ln 4

Answer 1

\[\frac{ -2 }{ 3 }\ln(k-8) + \frac{ 2 }{ 3 }\ln(k-1) = \ln4\]

Answer 2

Help Anyone?

Answer 3

can use ... ln x + ln y = ln xy

Answer 4

Yes I know that but how would you solve that?

(k-8)^-2/3 * (k-1)^2/3 = 4

Answer 5

can factor out 2/3 first...

Answer 6

How?

Answer 7

2/3 ln [-(k-8)(k-1)] = ln 4
2/3 ln [(-k+8)(k-1)] = ln 4
\[\sqrt[3]{(-k+8)^2(k-1)^2}=4\]

Answer 8

Hmmm ok.
But then if we're solving it don't we then get a quartic equation

Answer 9

\[(-k+8)(k-1)=\sqrt{4^3}\]

Answer 10

\[2/3(\ln(k-1)-\ln(k-8))=\ln4\] \[2/3\ln((k-1)/(k-8))=\ln4\]\[\ln((k-1)/(k-8))^2=\ln64\] \[((k-1)/(k-8))^2=64\] \[(k-1)/(k-8)=8\] \[k-1=8k-64\] \[63=7k\] \[k=9\]

Answer 11

Oh I see now! I just wasn't too sure about the indice changes.
Thanks to both of you!

Answer 12

np...