Answer: X is an exponent, and the correct answer is x ≈ 0.884228217
Explanation:
To solve for x in the equation 12^x = 9, you need to use logarithms. A logarithm is the inverse of an exponent. It tells you what power you need to raise a base to get a certain number. For example, log2(8) means “what power do you need to raise 2 to get 8?” and the answer is 3.
So, to solve 12^x = 9, you can take the logarithm of both sides with any base, such as 10 or e. For example, using base 10, you get:
log10(12^x) = log10(9)
Then, you can use the property of logarithms that says logb(a^c) = c * logb(a). This means you can bring down the x as a coefficient of the logarithm on the left side:
x * log10(12) = log10(9)
Then, you can divide both sides by log10(12) to isolate x:
x = log10(9) / log10(12)
Using a calculator, you can find that log10(9) is about 0.954242509 and log10(12) is about 1.079181246. So,
x = 0.954242509 / 1.079181246
x ≈ 0.884228217