If $$1$$,$$log3$$⁡$$31$$−$$x+2$$,$$log3$$⁡$$4.3x$$−$$1$$ are in A.P then, x equals:

Question

If $$1$$,$$log3$$⁡$$31$$−$$x+2$$,$$log3$$⁡$$4.3x$$−$$1$$ are in A.P then, x equals:

Infinity Learn · Accepted Answer

First of all logarithmic terms should have been defined, $$log3$$⁡$$31$$−$$x+2$$, so $$31$$−$$x+2$$>$$0$$ which is true ∀$$xlog3$$⁡$$4.3x$$−$$1$$, so $$log3$$⁡$$4.3x$$−$$1$$ thus $$3x$$>$$14$$ Now, terms are in A.P so, $$2log3$$⁡$$31$$−$$x+2=1+log3$$⁡$$4$$⋅$$3x$$−$$1=log3$$⁡$$3+log3$$⁡$$4.3x$$−$$1=log3$$⁡$$34.3x$$−$$131$$−$$x+22=34.3x$$−$$131$$−$$x+2=34.3x$$−$$1=12.3x$$−$$31313x+2=12$$⋅$$3x$$−$$3$$ Let $$t=3x3t+2=12t$$−$$3$$, so $$3+2t=12t2$$−$$3t12t2$$−$$5t+3=012t2$$−$$9t+4t$$−$$3=03t(4t$$−$$3)+1(4t$$−$$3)=0$$

$If 1, \log_{3} \sqrt{(3^{1 - x} + 2)}, \log_{3} ({4.3}^{x} - 1) are in A.P then, x equals:$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If 1,log3⁡31−x+2,log3⁡4.3x−1 are in A.P then, x equals:

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$If 1, \log_{3} \sqrt{(3^{1 - x} + 2)}, \log_{3} ({4.3}^{x} - 1) are in A.P then, x equals:$