Question

select the correct answer. which exponential equation is equivalent to this logarithmic equation? \\(\log_{2} x = 24\\) \\(\bigcirc\\) a. \\(2^{24} = x\\) \\(\bigcirc\\) b. \\(x^{24} = 2\\) \\(\bigcirc\\) c. \\(2^{x} = 24\\) \\(\bigcirc\\) d. \\(x^{2} = 24\\)

Explanation:

Step1: Recall log to exp conversion rule

For $\log_b a = c$, it converts to $b^c = a$.

Step2: Apply rule to given equation

Given $\log_2 x = 24$, here $b=2$, $c=24$, $a=x$.
So $2^{24} = x$.

Answer:

A. $2^{24} = x$