Solve for T. I'm stuck and can't remember (Super Easy ten points)?

Question

500= 1.259921^T

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

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

Take the log of both sides

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

Answer 5

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