What exponent would make the two expressions equivalent: (33)x=324 ?(1 point)
Responses
21
21
8
8
27
27
15
8
To find the exponent that would make the two expressions equivalent, we need to solve the equation (33)^x = 324.
Taking the logarithm of both sides (with any base), we can simplify the equation.
log((33)^x) = log(324)
Using the property of logarithms that states log(a^b) = b * log(a), we can rewrite the equation as:
x * log(33) = log(324)
Now, we can substitute the values into a calculator to find the logarithm of 33 and 324:
x * 1.5185 = 2.5092
Next, we can solve for x:
x ≈ 2.5092 / 1.5185
Therefore, the exponent that would make the two expressions equivalent is approximately 1.65.
To find the exponent that makes the two expressions equivalent, we need to solve for x in the equation (33)^x = 324.
Here's how you can solve it step by step:
1. Start by taking the logarithm of both sides of the equation. You can use either the natural logarithm (ln) or the common logarithm (log) depending on the calculator you have.
Assuming you are using the common logarithm, the equation becomes: log((33)^x) = log(324).
2. Apply the logarithmic property log(a^b) = b * log(a) to simplify the equation. This gives us: x * log(33) = log(324).
3. Now, plug the values into a calculator to find the logarithms.
log(33) ≈ 1.5185
log(324) ≈ 2.5105
4. Substitute these values back into the equation: x * 1.5185 = 2.5105.
5. Divide both sides of the equation by 1.5185: x ≈ 2.5105 ÷ 1.5185 ≈ 1.652.
So, the exponent that would make the two expressions equivalent is approximately 1.652.
Looking at the provided answer choices, the correct answer is not given. However, the correct exponent we found in our calculation is approximately 1.652.