Question

9th class question chapter 1 number system ​

Answer 1

$3^{4x +1} = ( \frac{1}{9} ^{x +1} )$

sentence on lhs the fraction is in form of $\frac{1}{n}$ so the power would be negative to make it without fraction.

$3^{4x + 1} = 9^{-x - 1}$

since 9 can be written as $3^2$

$3^{4x + 1} = 3^{2(-x -1)}$

$3^{4x + 1} = 3^{-2x - 2}$

cancelling out 3

$4x + 1 = -2x - 2$

$4x + 2x = -2 - 1$

$6x = -3$

$x = \frac{-3}{6}$

$x = -0.5$