SOLUTION: I have a question in regards to a problem that was already submitted and solved. THe question number is 149823, and it was solved by, vleith(790). THe question i have is around the

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Question 149931This question is from textbook college algebra
: I have a question in regards to a problem that was already submitted and solved. THe question number is 149823, and it was solved by, vleith(790). THe question i have is around the second problem. I am having trouble understanding how we got the equation or answer of (1-(0.5)^n/14)= 2.5/5.58, and the next step says -(0.5)^n/14 = -0.552. How did we get - 0.552? and i am hoping this will help me understand the rest of the this problem. but if there is anyway of explaining the following steps to solve for this would be helpful.
This question is from textbook college algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given expression.

Divide 2.5%2F5.58 to get 0.448

Subtract 1 from both sides.


Combine like terms.


Raise both sides to the 14th power. This eliminates the "14" in the denominator of the exponent.


Raise -0.552 to the 14th power to get 0.00024


Divide both sides by -1.


Take the log of both sides.


Rewrite the left side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


Divide both sides by log%2810%2C%280.5%29%29.



Evaluate log%2810%2C%280.00024%29%29%2Flog%2810%2C%280.5%29%29 with a calculator to get 12.025


So the approximate answer is n=12.025