🎥 Watch Video Solution
Q. If \( 9^{x+2} = 240 + 9^x \), find \( x \)
(a) 0.5 (b) 0.2 (c) 0.4 (d) 0.1
✏️ Solution
\( 9^{x+2} = 9^x \cdot 9^2 \)
\( = 81 \cdot 9^x \)
\( 81 \cdot 9^x = 240 + 9^x \)
\( 81 \cdot 9^x – 9^x = 240 \)
\( 80 \cdot 9^x = 240 \)
\( 9^x = 3 \)
\( 9 = 3^2 \Rightarrow (3^2)^x = 3 \)
\( 3^{2x} = 3^1 \)
\( 2x = 1 \)
\( x = 0.5 \)
Correct Option: (a) 0.5
\( \boxed{0.5} \)