Solve for x 3^x=1/9

Problem

3=1/9

Solution

1. Rewrite the fraction on the right side of the equation as a power with a positive exponent.

1/9=1/3

2. Apply the negative exponent rule, which states that 1/(an)=a(−n) to rewrite the expression.

1/3=3(−2)

3. Substitute this back into the original equation to set the bases equal to each other.

3=3(−2)

4. Equate the exponents since the bases are identical and positive (not equal to 1).

x=−2

Final Answer

3=1/9⇒x=−2

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