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Solve the equation log((x^(3)+6))(x^(2)-...

Solve the equation `log_((x^(3)+6))(x^(2)-1)=log_((2x^(2)+5x))(x^(2)-1)`

Text Solution

Verified by Experts

The equation is equivalent to
`{(x^(2)-1gt0),(2x^(2)+5xgt0),(2x^(2)+5x!=1),(x^(3)+6=2x^(2)+5x):}`
`implies{(xlt-1 "and"xgt1),(xlt-5/2"and"xgt0),(x!=(-5+-sqrt(3))/4),(x=-2,1,3):}`
Hence `x_(1)=3` is only root of the original equation.
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