Question

solve. write your answer as an integer or a fraction in simplest form. 1 = 9^{3x} x = \boxed{}

Explanation:

Step1: Recall the property of exponents

Any non - zero number raised to the power of 0 is 1, i.e., \(a^{0}=1\) for \(a
eq0\). We can rewrite the equation \(1 = 9^{3x}\) using this property. So we want to find \(x\) such that the exponent \(3x\) makes \(9^{3x}=1\). Since \(9
eq0\), we know that \(9^{0}=1\). So we can set the exponents equal to each other.

Step2: Set the exponents equal

We have the equation \(9^{3x}=9^{0}\). When the bases are the same (and the base is not 0 or 1), we can set the exponents equal to each other. So \(3x = 0\).

Step3: Solve for \(x\)

To solve for \(x\), we divide both sides of the equation \(3x=0\) by 3. \(\frac{3x}{3}=\frac{0}{3}\), which simplifies to \(x = 0\).

Answer:

\(0\)