SOLUTION: Solve for x: {{{log( 2, x+2)=log( .5, 2)}}}

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Question 116597: Solve for x:
log%28+2%2C+x%2B2%29=log%28+.5%2C+2%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%28+2%2C+x%2B2%29=log%28+.5%2C+2%29 Start with the given equation


log%28+2%2C+x%2B2%29=-1 Evaluate log%28+.5%2C+2%29 to get -1


2%5E%28-1%29=x%2B2 Rewrite the equation using the property: log%28b%2C%28x%29%29=y ====> b%5Ey=x


1%2F2%5E%281%29=x%2B2 Rewrite 2%5E%28-1%29 as 1%2F2%5E%281%29


1%2F2=x%2B2 Evaluate 1%2F2%5E%281%29 to get 1%2F2


1%2F2-2=x%2Bcross%282-2%29 Subtract 2 from both sides


-3%2F2=x Combine like terms

So our answer is x=-3%2F2