Solve for the unknown 243^(x-3)=9^x

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation to be solved for x is 243^(x - 3) = 9^x

Make the base 3 on both the sides

243 = 3^5 and 9 = 3^2

243^(x - 3) = 9^x

=> 3^5^(x - 3) = 3^2^x

=> 3^(5x - 15) = 3^2x

as the base is the same equate the exponent.

5x - 15 = 2x

=> 3x = 15

=> x = 5

The solution of the equation x = 5

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll create matching bases of exponentials from both sides, namely powers of 3.

243 = 3^5

9 = 3^2

We'll re-write the equation having common bases both sides:

3^5(x-3) = 3^2x

Since the bases are matching, we'll use the one to one property of exponentials and we'll get:

5(x-3) = 2x

We'll remove the brackets from the left side:

5x - 15 = 2x

We'll subtract 2x and add 15 both sides:

3x = 15

We'll divide by 3:

x = 5

The solution of the equation is x = 5.

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