SOLUTION: How do you solve the exponential equation -5e^-x+9=6

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Question 126824: How do you solve the exponential equation -5e^-x+9=6
Found 2 solutions by Earlsdon, solver91311:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
-5%2Ae%5E%28-x%29+%2B+9+=+6 Subtract 9 from both sides.
-5%2Ae%5E%28-x%29+=+-3 Divide both sides by -5.
e%5E%28-x%29+=+3%2F5
1%2Fe%5Ex+=+3%2F5 Invert both sides.
e%5Ex+=+5%2F3 Now take the natural log of both sides.
ln%28e%29%5Ex+=+ln%285%2F3%29
x%2Aln%28e%29+=+ln%285%2F3%29 But ln%28e%29+=+1, so...
x+=+0.512
Check:
-5%2Ae%5E%28-x%29+%2B+9+=+6 Substitute x = 0.512
-5%2Ae%5E%28-0.512%29+%2B+9+=+6
-5%2A0.6%2B9+=+6
-3%2B9+=+6
6+=+6

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
-5e%5E%28-x%29%2B9=6

-5e%5E%28-x%29=-3

e%5E%28-x%29=%28-3%29%2F-5

Now take the natural logarithm of both sides
log%28e%2Ce%5E%28-x%29%29=log%28e%2C3%2F5%29

Apply log%28b%2Cx%5Em%29=m%2Alog%28b%2Cx%29 and log%28b%2Ca%2Fc%29=log%28b%2Ca%29-log%28b%2Cc%29
-x%2Alog%28e%2Ce%29=log%28e%2C3%29-log%28e%2C5%29

log%28e%2Ce%29=1 so:
-x=log%28e%2C3%29-log%28e%2C5%29

Finally, multiply by -1
x=log%28e%2C5%29-log%28e%2C3%29