Solve for x 9^x=27

Problem

9=27

Solution

1. Identify a common base for both sides of the equation. Both 9 and 27 are powers of 3.

2. Rewrite the numbers using the base 3.

9=3

27=3

3. Substitute these expressions back into the original equation.

(3)x=3

4. Apply the power of a power rule, which states (am)n=a(m⋅n)

3(2*x)=3

5. Equate the exponents since the bases are now identical.

2*x=3

6. Solve for x by dividing both sides by 2.

x=3/2

Final Answer

9=27⇒x=3/2

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