InterviewSolution
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InterviewSolution
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Solve the equation `log_(1//3)[2(1/2)^(x)-1]=log_(1//3)[(1/4)^(x)-4]` |
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Answer» The given equation is equivalent to `{(2(1/2)^(x)-1gt0),(2(1/2)^(x)-1=(1/4)^(x)-4):}` `implies{((1/2)^(x)gt1/2),((1/2)^(2x)-2(1/2)^(x)-3=0):}` `implies{(xlt1),([(1/2)^(x)-3][(1/2)^(x)+1]):}=0` `implies{(xlt1),((1/2)^(x)=3,(1/2)^(x)+1!=0):}implies{(xlt1),(x=(-log_(2)3)):}` Hence `x_(1)=-log_(2)3` is the root of the original equation. |
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