Question

solve. write your answer as an integer or a fraction in simplest form.
1 = 8^(4x + 3)
x =

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 \(1 = 8^{4x + 3}\), we can rewrite 1 as \(8^0\) since \(8
eq0\). So the equation becomes \(8^0=8^{4x + 3}\).

Step2: Set the exponents equal

If two exponential expressions with the same base (where the base is a positive number not equal to 1) are equal, then their exponents are equal. Since the base 8 is a positive number not equal to 1, we can set the exponents equal to each other: \(0=4x + 3\).

Step3: Solve for x

Subtract 3 from both sides of the equation \(0 = 4x+3\):
\(0 - 3=4x+3 - 3\)
\(- 3 = 4x\)
Then divide both sides by 4:
\(x=\frac{-3}{4}\)

Answer:

\(-\frac{3}{4}\)