What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses
27
27
21
21
15
15
8
8
The correct answer is 8.
Which of the following describes one of the tasks of a good conclusion?(1 point)
Responses
going off on a tangent
going off on a tangent
summing up the passage
summing up the passage
providing a new piece of trivia
providing a new piece of trivia
making the reader angry
The correct answer is "summing up the passage."
In order to make the two expressions equivalent, we need to find the exponent that would make 33 raised to that exponent equal to 324.
To do this, we can use the property of exponents that states: a^b = c, where a is the base, b is the exponent, and c is the result.
So, we need to solve for the exponent in the equation (33)^x = 324.
To find the exponent, we can take the logarithm of both sides of the equation. Let's use the natural logarithm (ln) here:
ln((33)^x) = ln(324)
By applying the property of logarithms that states ln(a^b) = b * ln(a), the equation becomes:
x * ln(33) = ln(324)
Now we can solve for x by dividing both sides of the equation by ln(33):
x = ln(324) / ln(33)
Using a calculator, we can evaluate that:
x ≈ 3.1100
Therefore, the exponent that would make the two expressions equivalent is approximately 3.1100.
To find the exponent that would make the two expressions equivalent, we need to solve the equation (33)^x = 324.
To solve exponential equations like this, we can use logarithms. In this case, since the base of the exponent is 3, it is convenient to use logarithm with base 3.
Taking the logarithm of both sides of the equation, we get:
log3(33)^x = log3(324)
Using the logarithmic identity logb(a^c) = c * logb(a), we can simplify the equation to:
x*log3(33) = log3(324)
Now we can divide both sides of the equation by log3(33) to isolate x:
x = log3(324)/log3(33)
Using a calculator to evaluate the logarithms, we get:
x ≈ 4
Therefore, the exponent that would make the two expressions equivalent is 4.