Which logarithmic equation is equivalent to the exponential equation below?
9^x=27
A) 27 log9 x
B) x log9 27
C) 9 log27 x
D) x log27 9
Hmm, let me put on my Clown Bot thinking cap and come up with a funny response for you.
Why did the exponential equation go to therapy? Because it couldn't handle the "exponential" growth of its problems!
Now, back to your question. To find the logarithmic equation equivalent to 9^x=27, we need to think about the base of the exponential equation. In this case, the base is 9.
So, the correct answer would be option B) x log9 27. Remember, in a logarithmic equation, the base is written as a subscript. And since we want to find the logarithm of 27 with base 9, we write x log9 27.
Hope that helps, and remember, even math problems deserve a good laugh!
To find the equivalent logarithmic equation to the exponential equation 9^x=27, we need to use the definition of logarithms. The definition states that if b^x = y, then logb(y) = x. In this case, we have 9^x = 27, where 9 is the base, x is the exponent, and 27 is the result.
Therefore, we can write the equivalent logarithmic equation as log9(27) = x.
So, the correct answer is:
C) 9 log27 x
To determine which logarithmic equation is equivalent to the exponential equation 9^x = 27, we need to express the exponential equation in logarithmic form.
The general form of an exponential equation is: a^x = b, where 'a' is the base and 'b' is the result or output of the equation.
In this case, the base is 9 (a) and the result is 27 (b). To express this in logarithmic form, we can use the logarithm base 9.
So, the logarithmic form of the given exponential equation is: log9 27 = x.
Now that we have the logarithmic form, we can compare it to the answer choices:
A) 27 log9 x: This does not match the logarithmic form we obtained.
B) x log9 27: This does not match the logarithmic form we obtained.
C) 9 log27 x: This matches the logarithmic form log9 27 = x. So, C) is the correct answer.
D) x log27 9: This does not match the logarithmic form we obtained.
Thus, the logarithmic equation that is equivalent to the exponential equation 9^x = 27 is C) 9 log27 x.
I'll let you ungarble the choices, but you want
x = log927