To solve the logarithmic equation [tex]\(\log_2 x = 24\)[/tex], we need to convert it into an equivalent exponential form.
The general relationship between logarithms and exponents is given by:
[tex]\[ \log_b(y) = x \quad \text{is equivalent to} \quad b^x = y. \][/tex]
Here, the logarithmic equation given is [tex]\(\log_2 x = 24\)[/tex]. Using the relationship stated above:
1. The base [tex]\(b\)[/tex] is 2.
2. The exponent [tex]\(x\)[/tex] is 24.
3. The result [tex]\(y\)[/tex] is [tex]\(x\)[/tex].
Thus, we can convert [tex]\(\log_2 x = 24\)[/tex] to its exponential form as follows:
[tex]\[ 2^{24} = x. \][/tex]
So, the correct exponential equation that represents [tex]\(\log_2 x = 24\)[/tex] is:
[tex]\[ 2^{24} = x. \][/tex]
Now, let's match this with the given multiple-choice options:
A. [tex]\(2^{24} = x\)[/tex]
B. [tex]\(2^x = 24\)[/tex]
C. [tex]\(x^2 = 24\)[/tex]
D. [tex]\(x^{24} = 2\)[/tex]
Among these choices, the correct answer is:
A. [tex]\(2^{24} = x\)[/tex]
