If $$log2(5.2x+1)$$, $$log4(21$$−$$x+1)and$$ $$1$$ are in A.P, then x is equal to

Question

If $$log2(5.2x+1)$$, $$log4(21$$−$$x+1)and$$ $$1$$ are in A.P, then x is equal to

Infinity Learn · Accepted Answer

From the given condition, we must have           $$2log4(21$$−$$x+1)=log2(5.2x+1)+1$$⇒         $$2log4(21$$−$$x+1)log4=log2(5.2x+1)log2+1$$⇒         $$2log(21$$−$$x+1)log4=log(5.2x+1)log2+1$$⇒        $$log(21$$−$$x+1)=log$$[(5.2x+1)2$$]⇒         $$21$$−$$x+1=5.2x.2+2Now$$, put $$2x=y$$, so $$that2y+1=10y+2$$⇒  $$10y2+y$$−$$2=0$$⇒ $$(5y$$−$$2)(2y+1)=0Which$$ $$meansy=2/5$$  or  $$y=$$−$$1/2$$.  Since $$y=2xcannot$$ be negative, we $$havey=2x=2/5=0.4$$  ie.,  $$x=log2(0.4). But $$2x=2/5can$$ also express in the $$formx=log(2/5)log2=1$$−$$log5log2$$.

If $\log_{2} ({5.2}^{x} + 1), \log_{4} (2^{1 - x} + 1)$ and 1 are in A.P, then x is equal to

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If log2(5.2x+1), log4(21−x+1)and 1 are in A.P, then x is equal to

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If $\log_{2} ({5.2}^{x} + 1), \log_{4} (2^{1 - x} + 1)$ and 1 are in A.P, then x is equal to