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How do you solve #3^(x-2)=81#?

Answer 1

Elijah Allen

#x =6#

Learning the powers up to 1,000 is actually advantageous.

Two types of exponential equations exist.

those that require logs, those that can be completed mentally, or those that require very simple calculations

This one fits into the former category, where matching bases or indices are required.

Note: #3^4 = 81#

81 is therefore a power of three.

#3^(x-2) = 3^4" "larr# bases are equal, so the indices are equal.

#x-2 = 4#

#x =6#

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Answer 2

Chloe Alexander

To solve (3^{x-2} = 81), you need to isolate (x). First, rewrite (81) as a power of (3) since both sides of the equation have a base of (3).

[81 = 3^4]

Now, the equation becomes:

[3^{x-2} = 3^4]

Since the bases are the same, you can equate the exponents:

[x - 2 = 4]

Now, solve for (x):

[x = 4 + 2]

[x = 6]

So, the solution to the equation is (x = 6).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.