If $$1$$,$$log9(31$$−$$x+2)$$, $$log3(4.3x$$−$$1)$$ are in A.P, then x is equal to

Question

If $$1$$,$$log9(31$$−$$x+2)$$, $$log3(4.3x$$−$$1)$$     are in A.P, then x     is equal to

Infinity Learn · Accepted Answer

$$1$$,$$log9(31$$−$$x+2)$$, $$log3(4.3x$$−$$1)$$ are in A.P∴          $$2log9(31$$−$$x+2)=1+log3(4.3x$$−$$1)$$⇒          $$2log32(31$$−$$x+2)=log33+log3(4.3x$$−$$1)$$⇒          $$22log3(31$$−$$x+2)=log3(3{4.3x$$−$$1})$$⇒        $$31$$−$$x+2=3$$.(4.3x$$−$$1)⇒        $$3+2.3x=12.32x$$−$$3.3x$$⇒        $$12(3x)2$$−$$5(3x)$$−$$3=0$$∴               $$3x=3/4$$,  $$3x$$≠−$$1/3$$                    $$x=log34$$ $$3$$ $$=1$$−$$log34$$  .

If $1, \log_{9} (3^{1 - x} + 2), \log_{3} ({4.3}^{x} - 1)$ are in A.P, then $x$ is equal to

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If 1,log9(31−x+2), log3(4.3x−1) are in A.P, then x is equal to

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If $1, \log_{9} (3^{1 - x} + 2), \log_{3} ({4.3}^{x} - 1)$ are in A.P, then $x$ is equal to