What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses
21
21
15
15
27
27
8
8
To find the exponent that would make the two expressions equivalent, we need to determine which exponent we need to raise 33 to in order to obtain 324.
In this case, we need to find x.
To do this, we need to find the power that when applied to 33, will give us 324.
So, we need to solve the equation (33)^x = 324.
To find the exponent x, we can use logarithms.
Taking the logarithm base 33 of both sides of the equation, we have:
log33[(33)^x] = log33(324)
Using the property of logarithms that states loga(b^c) = c * loga(b), we can rewrite the equation as:
x * log33(33) = log33(324).
Since log33(33) is equal to 1, the equation becomes:
x = log33(324).
Using a calculator to evaluate log33(324), we find that x is approximately 2.
Therefore, the correct exponent that would make the two expressions equivalent is 2.
To find the exponent that would make the two expressions (33)^x and 324 equivalent, we need to calculate the value of x by taking the logarithm.
First, take the logarithm of both sides of the equation: log[(33)^x] = log(324).
Using the logarithmic property log(a^b) = b * log(a), we can rewrite the left side of the equation as x * log(33): x * log(33) = log(324).
Now, divide both sides of the equation by log(33): x = log(324) / log(33).
Using a calculator or mathematical software, we can compute the logarithm of 324 divided by the logarithm of 33.