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The number of value(s) of x satisfying 1-log_(g)(x+1)^(2)=1/2log_(sqrt(3))((x+5)/(x+3)) is |
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Answer» `=1-2/2log_(3)|x+1|2/2=log_(3)((x+5)/(x+3))` `=log_(3)(3/(|x+1|))=log_(3)((x+5)/(x+3))` `implies3/(|x+1|)=(x+5)/(x+3)` Case I1 `x+1gt0impliesxgt-1` `implies3(x+3)=(x+1)(x+5)` `impliesx^(2)+3x-4=0` `impliesx=-4` or `x=1` `x=-4` rejected `(xgt-1)` `:.x=1` Case II `x+1lt0impliesxlt-1` `3(x+3)-1(x+1)(x+5)` `impliesx^(2)+9x+14=0` `impliesx=-2` or `x=-7` `:.` Set of value of `x` `={-7, -2, 1}` |
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