Question Details

The real root of the equation 26x+23x+2-21=0 is

Options

A

log27

B

log29

C

log23/3

D

log227

Show Answer

Correct Answer :

Option C

log23/3

Solution :

Let the given equation be:
22x32x+1+8=0

We can rewrite the equation as:
(2x)26(2x)+8=0

Let y=2x. Then, the quadratic equation becomes:
y26y+8=0

Factoring the quadratic equation:
(y2)(y4)=0

This gives:
y=2 or y=4

Substituting back y=2x:
2x=2x=1
2x=4x=2

Thus, the roots are x=1 (which is log22) and x=2 (which is log24). Based on the scrambled options in the PDF, if the equation was meant to have a different constant, the standard substitution method applies. For the transcribed equation, the roots are 1 and 2.

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