Question

3^2x-1 - 9^x-1=1428 find x<br />${3}^{2x - 1} - {9}^{x - 1} find \: x$<br />​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

4

Step-by-step explanation:

Note: In my view you copied the question wrong as 1428 cannot be converted to exponential form of 3.  Factors of `1428 = 3*2*2*7*17.

Thus as you can see this will not work as you need to have the RHS number which is 3 raised to some power. In my view the the number on R.H.S should be 1458 (i.e. 3⁸). I will solve the question with RHS as 1458 but please note the method to solve is the same.  

3^2x-1 - 9^x-1=1458

3^2x-1 - (3²)^x-1 = 1458.

3^2x-1 - 3^2x-2 = 1458.

3^2x/3 - 3^2x/9 = 1458

Let 3ˣ = y

y²/3 - y²/9 = 1458

3y² - y²/9 = 1458

2y² = 1458*9 = 13122

y² = 1458*9/2 = 6561 .

But y = 3ˣ

=> 3^2x = 3⁸

When bases are same powers are equal.

=> 2x = 8

=> x = 4.