Question

solve. write your answer as an integer or a fraction in simplest form. 1 = 8^{x - 1} x = \boxed{} \frac{\square}{\square} submit

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 \(a
eq0\). In the equation \(1 = 8^{x - 1}\), we can rewrite 1 as \(8^0\) (since \(8
eq0\) and \(8^0=1\)). So the equation becomes \(8^0=8^{x - 1}\).

Step2: Set the exponents equal

If two exponential expressions with the same base (and the base is non - zero) are equal, then their exponents are equal. Since the base 8 is non - zero and \(8^0 = 8^{x-1}\), we can set the exponents equal to each other: \(0=x - 1\).

Step3: Solve for x

To solve for x, we add 1 to both sides of the equation \(0=x - 1\). Adding 1 to both sides gives \(x=0 + 1=1\).

Answer:

\(1\)