SOLUTION: Find all solutions of the equation e^x − 30 e^(−x) = −7 If there is more than one answer, enter them in a list separated by commas. IMPORTANT: Decimal answe

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find all solutions of the equation e^x − 30 e^(−x) = −7 If there is more than one answer, enter them in a list separated by commas. IMPORTANT: Decimal answe      Log On


   

Question 951878: Find all solutions of the equation
e^x − 30 e^(−x) = −7

If there is more than one answer, enter them in a list separated by commas. IMPORTANT: Decimal answers will be marked incorrect. Enter an EXACT, symbolic answer (such as 3/2, not 1.5, or ln(2), not .693)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+e%5Ex+-+30e%5E%28-x%29+=+-7+
Multiply both sides by +%281%2F30%29%2Ae%5Ex+
+%281%2F30%29%2Ae%5E%282x%29+-+1+=+-7%2A%281%2F30%29%2Ae%5Ex+
+%281%2F30%29%2Ae%5E%282x%29+%2B+7%2A%281%2F30%29%2Ae%5Ex+-+1+=+0+
+e%5E%282x%29+%2B+7e%5Ex+-+30+=+0+
+%28+e%5Ex+%2B+10+%29%2A%28+e%5Ex+-+3+%29+=+0+
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+e%5Ex+=+-10+
Take the natural log of both sides
+x+=+ln%28-10%29+
There is no log to the base e that gives
a negative number, so I can' t solve this
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+e%5Ex+=+3+
+x+=+ln%283%29+
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check:
+e%5Ex+-+30e%5E%28-x%29+=+-7+
+3+-+30%2A%28+1%2F3%29+=+-7+
+3+-+10+=+-7+
+-7+=+-7+
OK