Question

The real root of the equation \(2^{6x}+2^{3x+2}-21=0\) is

• A. \(\frac{log_27}{3}\)
• B. \(log_2\ 9\)
• C. \(\frac{log_2\ 3}{3}\)
• D. \(log_2\ 27\)

Answer 1

The Correct Option is C

\(2^{6x}+2^{3x}×2^2−21=0\)
Take \(2^{3x}=y\)
\(⇒y^2+4y−21=0\)
\(⇒(y−3)(y+7)=0\)
\(⇒y=3 \ or\ y=−7\)
\(⇒2^{3x}=3 \ or\ 2^{3x}=−7\){ No solution }
\(⇒3x=log_23\)
\(⇒x=\frac{log_23}{3}\)