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What is 9^x=3?

Option 1: x=1/2
Option 2: x=2
Option 3: x=3
Option 4: x=4

User Glory Raj
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1 Answer

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Final answer:

To solve 9^x = 3, rewrite 9 as 3^2, giving (3^2)^x = 3. By the power rule, 3^(2x) = 3^1, and equating exponents gives x = 1/2, which corresponds to Option 1.

Step-by-step explanation:

Finding the Value of x in 9^x = 3

To solve the equation 9^x = 3, we need to express both sides of the equation with the same base. Since 9 is 3 squared (3^2), we can rewrite the equation as (3^2)^x = 3. Applying the power rule of exponents, which states that (a^b)^c = a^(b*c), we get 3^(2x) = 3^1. Because the bases are now the same, the exponents must be equal for the equation to hold true, so 2x = 1. Dividing both sides by 2 gives us x = 1/2, which is Option 1.

This process demonstrates the use of exponent rules and understanding of fractional powers to solve equations involving exponents.

User Mithun Shreevatsa
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