SOLUTION: {{{ ln(t/(t-4))=1 }}} solve for t. give exact answer. (no decimals) thank you    ∆  ∆ ∆

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: {{{ ln(t/(t-4))=1 }}} solve for t. give exact answer. (no decimals) thank you    ∆  ∆ ∆      Log On


   

Question 365680: +ln%28t%2F%28t-4%29%29=1+
solve for t. give exact answer. (no decimals)
thank you
   ∆
 ∆ ∆
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+ln%28t%2F%28t-4%29%29=1+ Start with the given equation.


+ln%28t%2F%28t-4%29%29=ln%28e%29+ Rewrite 1 as ln%28e%29. Recall that ln%28e%29=1


Since the logs have the same base (e), this means that the arguments (the stuff inside the logs) are equal.


Formally, if ln%28x%29=ln%28y%29, then x=y


+t%2F%28t-4%29=e+ Use the property given above to set the arguments equal to each other.


+t=e%28t-4%29+ Multiply both sides by t-4.


+t=et-4e+ Distribute.


+t-et=-4e+ Subtract et from both sides.


+t%281-e%29=-4e+ Factor out the GCF 't'.


+t=-4e%2F%281-e%29+ Divide both sides by 1-e to isolate 't'.


Optional Step: You can rewrite 1-e as -e%2B1=-%28e-1%29 and notice how the negatives cancel in the numerator and denominator. So t=4e%2F%28e-1%29 also


So the solution is +t=-4e%2F%281-e%29+


You can also write the solution as t=4e%2F%28e-1%29 (the two are equivalent).


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim