Question

Solve for x
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Answer 1

Any choices?

Answer 2

\[\large\rm 3^{x-1}=(\color{orangered}{9})^{x-2}\]

Recall that 9 is a power of 3. It's 3 squared.

\[\large\rm 3^{x-1}=(\color{orangered}{3^2})^{x-2}\]

One of our exponent rules tell us how to apply an exponent and an exponent.
\(\rm (a^b)^c=a^{bc}\)

We multiply the exponents.

So for our problem, we should expect this change to occur on the right side,
\[\large\rm 3^{x-1}=3^{2(x-2)}\]
The 2 exponent and the (x-2) exponent are multiplying.

Now that your exponentials have the `same base`,
you can equate the exponents:

x-1 = 2(x-2)

And then solve for x using basic Algebra steps.