Final answer:
To solve the equation 3^2x=6,561, we can take the logarithm of both sides and simplify the equation.
Step-by-step explanation:
To solve the equation 32x=6,561, we need to isolate the variable x. We can do this by taking the logarithm of both sides of the equation. The base of the logarithm can be any positive number, but the most commonly used bases are 10 (common logarithm) and e (natural logarithm).
Using the natural logarithm (ln) as the base, we have:
ln(32x) = ln(6,561)
Applying the logarithm power rule, which states that ln(ab) = b * ln(a), we can simplify the left side of the equation:
2x * ln(3) = ln(6,561)
Finally, we divide both sides of the equation by ln(3) to solve for x:
x = ln(6,561) / (2 * ln(3))
Using a calculator or computer software, we can find that x is approximately 4.0765.