# quick algebra solving equation problem

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• Feb 9th 2007, 03:11 PM
checkmarks
quick algebra solving equation problem
please help:

1) 275 = 150 (1+x)^16
how do i solve for x?

2) 500 = 100 (1+0.065/2)^n
solve for n

thank you
these are compound interest problems if ur wondering.
• Feb 9th 2007, 04:11 PM
ticbol
Quote:

Originally Posted by checkmarks
please help:

1) 275 = 150 (1+x)^16
how do i solve for x?

2) 500 = 100 (1+0.065/2)^n
solve for n

thank you
these are compound interest problems if ur wondering.

1.) 275 = 150(1+x)^16
275/150 = (1+x)^16
Raise both sides to their 1/16th power,
(275/150)^(1/16) = 1+x
1.038610215 = 1 +x
x = 0.038610215 ---------------answer.

Another way, using logarithms:
275 = 150(1+x)^16
275/150 = (1+x)^16
1.833333333 = (1+x)^16
Take the natural logs of both sides, -----(use common logs if you like).
Ln(1.8333333333) = 16Ln(1+x)
0.606135804 = 16Ln(1+x)
Divide both sides by 16,
0.037883488 = Ln(1+x)
e^0.037883488 = 1+x
1.038610215 = 1+x
x = 0.038610215 -----------same as above.

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2) 500 = 100 (1+0.065/2)^n

Here you'd be forced to use logarithms only.

Divide both sides by 100,
5 = (1.0325)^n
Ln(5) = n*Ln(1.0325)
n = Ln(5) / Ln(1.0325)
n = 50.32159601 -----------------answer.