Split - Evaluate "t" from Ln function

[haiderali]

i think i wrote it wrong ..

but can anyone tell me what is the value of "t" using this equation :

ln(sqrt(1/2t)) = ( ln|x| ) + c ??

 

[JeffM]

i think i wrote it wrong ..

but can anyone tell me what is the value of "t" using this equation :

ln(sqrt(1/2t)) = ( ln|x| ) + c ??

\(\displaystyle e^{c} = k \implies k > 0\ and\ c = ln(k).\)

\(\displaystyle ln\left(\sqrt{\dfrac{1}{2t}}\right) = ln(|x|) + c = ln(|x|) + ln(k) = ln(k|x|) \implies\)

\(\displaystyle \sqrt{\dfrac{1}{2t}} = k|x| \implies \dfrac{1}{2t} = k^2x^2 \implies t = \dfrac{1}{2k^2x^2}.\)

 

[HallsofIvy]

i think i wrote it wrong ..

but can anyone tell me what is the value of "t" using this equation :

ln(sqrt(1/2t)) = ( ln|x| ) + c ??

?? "t" is a variable. It does not have any single value.

 

[Deleted member 4993]

i think i wrote it wrong ..

but can anyone tell me what is the value of "t" using this equation :

ln(sqrt(1/2t)) = ( ln|x| ) + c ??

Is it:

\(\displaystyle {\displaystyle ln \left [\sqrt{\frac {1}{2t}}\right ] \ = \ ln(|x|)}\)

or

\(\displaystyle {\displaystyle ln \left [\sqrt{\frac {1}{2}t}\right ] \ = \ ln(|x|)}\) .....← ..... your post indicates this equation to be solved for 't'.