Question

if 3 to the power 2 X + 1 / 9 is equal to 27 find the value of x

Answer 1

Hello friends!!

Here is your answer :

${3}^{2x + \frac{1}{9} } = 27$


First we find prime factors of 27

$3 |27 \\ 3 |9 \\ 3 |3 \\ \: \: |1$



Prime factors of 27 = 3 × 3 × 3

We can also write 27 as 3³.


${3}^{2x + \frac{1}{9} } = {3}^{3}$


When the bases are same, then their powers must be equal.


$2x + \frac{1}{9} = 3$


$2x = 3 - \frac{1}{9}$

$2x = \frac{27 - 1}{9}$


$2x = \frac{26}{9}$


$x = \frac{26}{9 \times 2}$


$x = \frac{13}{9}$



Hope it helps you..

Answer 2

${3}^{ \frac{2x+ 1}{9} } = {3}^{3} \\ \\ equal \: bases \: have \: equal \: powers \\ \\ \\ \\ \frac{2x + 1}{9} = 3 \\ \\ 2x + 1 = 27 \\ 2x = 27 - 1 = 26 \\ \\ x = \frac{26}{2} = 13$


I hope this will help you

-by ABHAY