SOLUTION: Solve 12^t-4 = 17^-3t for t using logarithms.

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Question 1198531: Solve 12^t-4 = 17^-3t for t using logarithms.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

12%5E%28t-4%29+=+17%5E%28-3t%29 for t using logarithms


log%2812%5E%28t-4%29+%29=+log%2817%5E%28-3t%29+%29

%28t-4%29log%2812+%29=-3t%2A+log%2817%29

%28t-4%29%2F%28-3t%29=+log%2817%29%2Flog%2812+%29

4%2F%283t%29+-+1%2F3=+log%2817%29%2Flog%2812+%29

4%2F%283t%29+=+log%2817%29%2Flog%2812+%29%2B1%2F3

4%2F%28log%2817%29%2Flog%2812+%29%2B1%2F3%29=+%283t%29+

t=4%2F%283%28log%2817%29%2Flog%2812+%29%2B1%2F3%29%29

t=%284log%2812%29%29%2F%28log%2812%29+%2B+3log%2817%29%29

t+=+%284+log%2812%29%29%2Flog%2858956%29.....exactly

t+=+0.904873627....approx.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Solve 12^t-4 = 17^-3t for t using logarithms.
A LOT of UNNECESSARY back-and-forth RUBBISH from that other person who responded.
   If matrix%281%2C3%2C+12%5E%28t+-+4%29%2C+%22=%22%2C+17%5E%28-+3t%29%29, then:
  ----- Taking log of both sides
 ----- Applying matrix%281%2C3%2C+log+%28%28a%29%29%5Eb%2C+%22=%22%2C+b%2Alog+%28%28a%29%29%29 
        
    - 3t(1.14) = t - 4 ------ Cross-multiplying and rounding 1.140168925, down to 2 decimal places
   - 3.42t - t = - 4
       - 4.42t = - 4
           

           THAT'S IT!!