SOLUTION: 12^(m+5)=17

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Question 156857: 12^(m+5)=17
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
12%5E%28m%2B5%29=17 Start with the given equation


log%2810%2C%2812%5E%28m%2B5%29%29%29=log%2810%2C%2817%29%29 Take the log of both sides


%28m%2B5%29%2Alog%2810%2C%2812%29%29=log%2810%2C%2817%29%29 Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


m%2B5=log%2810%2C%2817%29%29%2Flog%2810%2C%2812%29%29 Divide both sides by log%2810%2C%2812%29%29


m%2B5=log%2812%2C%2817%29%29 Use the change of base formula to rewrite the right side


m=log%2812%2C%2817%29%29-5 Subtract 5 from both sides


m=-3.85983 Use a calculator to evaluate the right side


So the exact answer is m=log%2812%2C%2817%29%29-5 which approximates to m=-3.85983

Answer by Edwin McCravy(6939) About Me  (Show Source):
You can put this solution on YOUR website!
Edwin's solution:

You don't need to go into logs in base 12, just use 
natural logs:

12%5E%28m%2B5%29=17

Take natural logs of both sides

ln%2812%5E%28m%2B5%29%29=ln%2817%29

Use the rule ln%28A%5EC%29=C%2Aln%28A%29 on the left:

%28m%2B5%29ln%2812%29=ln%2817%29

Divide both sides by ln%2812%29

m%2B5=ln%2817%29%2Fln%2812%29

Add -5 to both sides

m=ln%2817%29%2Fln%2812%29-5 or

m=-3.859831075

Edwin