SOLUTION: Solve for x using logs. 8^x = e^x+8. round to the nearest two decimal places.

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Question 782294: Solve for x using logs.
8^x = e^x+8.
round to the nearest two decimal places.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x using logs.
Assume the problem is
8%5Ex = e%5E%28%28x%2B8%29%29
Using natural logs we have
x*ln(8) = (x+8)*ln(e)
the ln of e is one so we have
x*ln(8) = x + 8
ln(8) = %28%28x%2B8%29%29%2Fx
Find the ln of 8
2.079 = %28x%2B8%29%29%2Fx
mult both sides by x
2.079x = x + 8
2.079x - x = 8
1.079x = 8
x = 8%2F1.079
x = 7.414
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Check this on your calc
enter 8^7.414 = 4960314
enter e^(7.414+8) = 4945556, (log inaccuracy)