SOLUTION: a. Solve for x b. Rewrite the answer so that each individual logarithm from part a is written as a sum or difference of logarithms of prime numbers {{{ 5/(3-e^(-x)) = 7 }}}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: a. Solve for x b. Rewrite the answer so that each individual logarithm from part a is written as a sum or difference of logarithms of prime numbers {{{ 5/(3-e^(-x)) = 7 }}}      Log On


   

Question 476213: a. Solve for x
b. Rewrite the answer so that each individual logarithm from part a is written as a sum or difference of logarithms of prime numbers
+5%2F%283-e%5E%28-x%29%29+=+7+
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
a. +5%2F%283-e%5E%28-x%29%29+=+7+ multiply both sides by %283-e%5E%28-x%29%29
+5=+7%2A%283-e%5E%28-x%29%29++divide by 7
3-e%5E%28-x%29+=5%2F7 subtract 3
-e%5E%28-x%29+=5%2F7-3 divide by -1
e%5E%28-x%29+=-5%2F7%2B3
e%5E%28-x%29+=16%2F7 logarithm
-x=ln%2816%2F7%29 divide by -1
x=-ln%2816%2F7%29
If use the scintific calculator x=-0.8267
.
b. Rewrite the answer so that each individual logarithm from part a is written as a sum or difference of logarithms of prime numbers
x=-ln%2816%2F7%29
Use formula ln%28a%2Fb%29=lna-lnb
x=-%28ln16-ln7%29
x=ln7-ln16