Question

If a power x-3 = 1/a power x-1 . What is the value of x?

Answer 1

The value of x in the given equation is 2

Solving Linear Equations

From the question, we are to determine the value of x in the given equation

The given equation is

a power x-3 = 1/a power x-1

That is,

$a^{x-3} =(\frac{1}{a} )^{x-1}$

Solving the equation,

$a^{x-3} =(\frac{1}{a} )^{x-1}$

$a^{x-3} =(a^{-1} )^{x-1}$

$a^{x-3} =a^{-x + 1}$

Now,

Since the bases are equal, we can equate the powers

That is,

x - 3 = -x + 1

Now, solve for x

x - 3 = -x + 1

x + x = 1 +  3

2x = 4

x = 4/2

x = 2

Hence, the value of x in the given equation is 2

Learn more on Solving linear equations here: brainly.com/question/723406

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