The roots of the equation {{3}^{2x}}-{{10.3}^{x}}+9
=0 are
A) 1, 2 B) 0, 2 C) 0, 1 D) 1, 3
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Hi ,
3^2x - 10 × 3^x + 9 = 0
3^2x - 3^x - 9 × 3^x + 9 = 0
3^x ( 3^x - 1 ) - 9 ( 3^x - 1 ) = 0
( 3^x - 1 )( 3^x - 9 ) = 0
Therefore ,
3^x - 1 = 0 or 3^x - 9 = 0
3^x = 1 or 3^x = 9
3^x = 3^0 or 3^x = 3²
x = 0 or x = 2
Option ( B ) is correct.
I hope this helps you.
: )
3^2x - 10 × 3^x + 9 = 0
3^2x - 3^x - 9 × 3^x + 9 = 0
3^x ( 3^x - 1 ) - 9 ( 3^x - 1 ) = 0
( 3^x - 1 )( 3^x - 9 ) = 0
Therefore ,
3^x - 1 = 0 or 3^x - 9 = 0
3^x = 1 or 3^x = 9
3^x = 3^0 or 3^x = 3²
x = 0 or x = 2
Option ( B ) is correct.
I hope this helps you.
: )
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