Connect with knowledgeable individuals and find the best answers at IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

Select the correct answer.

Which exponential equation is equivalent to this logarithmic equation?
[tex]\[ \log_2 x = 24 \][/tex]

A. [tex]\(x^2 = 24\)[/tex]

B. [tex]\(2^{24} = x\)[/tex]

C. [tex]\(2^x = 24\)[/tex]

D. [tex]\(x^{24} = 2\)[/tex]


Sagot :

To solve the problem of converting the logarithmic equation [tex]\(\log_2 x = 24\)[/tex] into an equivalent exponential equation, we need to use the properties of logarithms and exponentials.

The logarithmic equation [tex]\(\log_b a = c\)[/tex] can be rewritten as [tex]\(b^c = a\)[/tex]. Here, [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(a\)[/tex] is the argument (or the value inside the logarithm), and [tex]\(c\)[/tex] is the result of the logarithm.

Applying this property to the given equation:

- The base [tex]\(b\)[/tex] is 2.
- The result [tex]\(c\)[/tex] is 24.
- The argument [tex]\(a\)[/tex] is [tex]\(x\)[/tex].

So, using the property of logarithms:

[tex]\[ b^c = a \implies 2^{24} = x \][/tex]

This is the equivalent exponential equation. Therefore, the correct answer is:

B. [tex]\(2^{24} = x\)[/tex]

As we calculated, the value of [tex]\(2^{24}\)[/tex] is 16777216, which confirms our understanding and transformation from the logarithmic form to the exponential form.