SOLUTION: i do not know how to solve equations where there is a negative exponent. im sorry, i didnt know how to make the x negative to show it to you, but it's supposed to be {{{(2^x)+1=6}

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: i do not know how to solve equations where there is a negative exponent. im sorry, i didnt know how to make the x negative to show it to you, but it's supposed to be {{{(2^x)+1=6}      Log On


   

Question 176028: i do not know how to solve equations where there is a negative exponent. im sorry, i didnt know how to make the x negative to show it to you, but it's supposed to be
%282%5Ex%29%2B1=6


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
So the equation is 2%5E%28-x%29%2B1=6 ???


2%5E%28-x%29%2B1=6 Start with the given equation.


2%5E%28-x%29=6-1 Subtract 1 from both sides.


2%5E%28-x%29=5 Combine like terms.


1%2F2%5Ex=5 Flip the base of 2%5E%28-x%29 to get 1%2F2%5Ex


1=5%2A2%5Ex Multiply both sides by 2%5Ex.


1%2F5=2%5Ex Divide both sides by 5.


log%2810%2C%281%2F5%29%29=log%2810%2C%282%5Ex%29%29 Take the log of both sides.


log%2810%2C%281%2F5%29%29=x%2Alog%2810%2C%282%29%29 Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


log%2810%2C%281%2F5%29%29%2Flog%2810%2C%282%29%29=x Divide both sides by log%2810%2C%282%29%29.


log%282%2C%281%2F5%29%29=x Use the change of base formula to simplify the left side.


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Answer:

So the solution is x=log%282%2C%281%2F5%29%29


Note: some books may simplify log%282%2C%281%2F5%29%29 to get log%282%2C%281%2F5%29%29=log%282%2C%285%5E%28-1%29%29%29=-log%282%2C%285%29%29. So the answer (for some books) may be x=-log%282%2C%285%29%29