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500= 1.259921^T

Please tell me how to separate out the T in steps.
I just can't remember the process

2007-09-19 11:58:17 · 5 answers · asked by ~Bagon~ 2 in Science & Mathematics Mathematics

5 answers

By definition of the logarithm, a = b^c is the same as log [base b] (a) = c. So here log [ base 1.259921 ] (500) = T. Remember that for any base, log [base b] (a) = log [base c] (a) / log [base c] (b). So use you use your standard base-10 log on your calculator to calculate log(500) / log(1.259921). Or for that matter, you could just as well use the natural log and take ln(500) / ln(1.259921). It's the same answer either way.

Another way to solve this is to use the fact that log(a^b) = b log(a). So taking the log of both sides (any base, so long as it's consistant) gives you log(500) = T * log(1.259921) which you can easily solve for T.

2007-09-19 12:03:14 · answer #1 · answered by Anonymous · 0 0

Take the natural log of both sides:

ln 500 = ln (1.259921^T)

Use the laws of logarithms to extract T and divide:

ln 500 = T ln 1.259921

T = ln 500/ln 1.259921 ≈ 26.89736

2007-09-19 12:03:53 · answer #2 · answered by Pascal 7 · 0 0

Whenever the unknown is an exponent think of using logs - always:
ln500 = ln1.259921^T = Tln1.2...
So T = ln500/ln1.2...
This is from lnx^r =rlnx

2007-09-19 12:06:16 · answer #3 · answered by rrsvvc 4 · 0 0

Take the log of both sides

ln(500) = t * ln(1.25992)
t = ln(500)/ln(1.25992)
t = 26.9

2007-09-19 12:04:03 · answer #4 · answered by Anonymous · 0 0

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2007-09-19 12:03:47 · answer #5 · answered by Emmie 4 · 0 1

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