This question was asked in CAT-2019
The real root of the equation 26x + 23x+2 - 21 = 0 is..
Given equation - 26x + 23x+2 - 21 = 0
The idea is to convert the above equation to a quadratic one.
So, 26x = (23x)2
Let y = 23x
Now, 26x + 23x+2 - 21 = 0 can be rewritten as (23x)2+ 22.23x - 21 = 0
y2 + 4y - 21 = 0
Solving the above quadratic equation,
(y + 7) (y - 3) = 0
So, y = -7 or +3
y = 23x=> y should always be positive
Therefore, y = -7 is not a valid solution. So, only y = +3 exists.
Taking log on both sides,
log223x = log23
3x = log23
x = (log23)/3