Solveeit Logo
Login

Question

Quantitative Aptitude Question on Square and Square Roots

The real root of the equation 26x+23x+2−21=02^{6x}+2^{3x+2}-21=0 is

A

log273\frac{log_27}{3}

B

log2 9log_2\ 9

C

log2 33\frac{log_2\ 3}{3}

D

log2 27log_2\ 27

Answer

log2 33\frac{log_2\ 3}{3}

Explanation

Solution

26x+23x×22−21=02^{6x}+2^{3x}×2^2−21=0
Take 23x=y2^{3x}=y
⇒y2+4y−21=0⇒y^2+4y−21=0
⇒(y−3)(y+7)=0⇒(y−3)(y+7)=0
⇒y=3 or y=−7⇒y=3 \ or\ y=−7
⇒23x=3 or 23x=−7⇒2^{3x}=3 \ or\ 2^{3x}=−7{ No solution }
⇒3x=log23⇒3x=log_23
⇒x=log233⇒x=\frac{log_23}{3}