SOLUTION: 17=13.46(1.03)^t Show work and explain please :) I really don't understand how to solve this problem!

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Question 938288: 17=13.46(1.03)^t
Show work and explain please :) I really don't understand how to solve this problem!
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Logarithm skills are necessary. Understanding exponential functions must be assumed.

Pick your base, preferably e or 10.

log%2810%2C17%29=log%2810%2C%2813%2A1.03%5Et%29%29

log%2810%2C17%29=log%2810%2C13%29%2Blog%2810%2C%281.03%5Et%29%29

log%2810%2C17%29-log%2810%2C13%29=log%2810%2C%281.03%5Et%29%29

t%2Alog%2810%2C1.03%29=log%2810%2C17%29-log%2810%2C13%29

highlight%28t=%28log%2810%2C17%29-log%2810%2C13%29%29%2Flog%281.03%29%29
which can also be shown as
highlight%28t=log%2810%2C%2817%2F13%29%29%2Flog%2810%2C1.03%29%29

Use either a calculator or a table of logarithms to finish computing.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

17=13.46(1.03)^t
Show work and explain please :) I really don't understand how to solve this problem!
17+=+13.46%281.03%29%5Et

17%2F13.46+=+1.03%5Et ------------ Exponential form

log+%281.03%2C+%2817%2F13.46%29%29+=+t ------ Logarithmic form

t+=+log+%2817%2F13.46%29%2Flog+1.03 ------------- Applying change of base

t+=+7.899204 ≈ highlight_green%28t+=+7.9%29        

You can do the check!! 

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