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Algebra

Number of Solutions

MMTS_Full_Test_14

Grade 12

Question:

Number of real solutions of $2^x+3^x-4^x+6^x-9^x=1$

2

1

0

3

Step-by-Step Solution

Key Concept: Let $a=2^x,b=3^x$; equation is $a+b-a^2+ab-b^2=1$

$x=0$: $1+1-1+1-1=1$ ✓. Check if unique: for $x>0$ LHS behavior, for $x<0$. Unique solution.

Correct Answer: 4