What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses
21
21
8
8
27
27
15
To find the exponent that would make the two expressions equivalent, you need to solve the equation (33)x = 324.
To do this, you need to find the common logarithm of both sides of the equation.
log(33)x = log(324)
Now you can apply the power rule of logarithms to bring the exponent down as a coefficient:
x * log(33) = log(324)
Next, divide both sides of the equation by log(33) to isolate the variable x:
x = log(324) / log(33)
Using a calculator, you can calculate the values of log(324) and log(33) and then divide them to find the value of x.
The correct response from the given options would be:
8
To find the exponent that would make the two expressions equivalent, we need to solve the equation (33)^x = 324.
The first step is to recognize that 33 can be written as 3^2 * 11. So, the equation becomes (3^2 * 11)^x = 324.
Next, we can simplify the equation by raising each factor to the power of x: 3^(2x) * 11^x = 324.
Now, we can start to solve the equation by breaking down 324 into its prime factorization: 324 = 2^2 * 3^4.
Comparing the prime factorizations of both sides of the equation, we can set up the following equation for the exponents:
2x = 4 and x = 4.
Therefore, the exponent that would make the two expressions equivalent is x = 4.
Looking at the given options, none of them have an exponent of 4. So none of the provided options is correct.