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ANSWER
D.
EXPLANATION
If
[tex] ln(x) = y[/tex]
Then solving for x will gives us:
[tex] {e}^{ ln(x) } = {e}^{y} [/tex]
[tex]x = {e}^{y} [/tex]
This first pair are equivalent:
If
[tex]log_{b}(N)= P[/tex]
we
Then,
[tex] {b}^{log_{b}(N) = {b}^{ P}} [/tex]
[tex]N= {b}^{ P}[/tex]
This pairs are also equivalent.
If
[tex]x = \sqrt{y} [/tex]
Then we rewrite as an index to obtain;
[tex]x = {y}^{ \frac{1}{2} } [/tex]
This pair is also equivalent.
[tex]log_{p}(N)= b[/tex]
Then
[tex] {p}^{log_{p}(N)} = {p}^{b} [/tex]
[tex] {p}^{b} = N[/tex]
But this was not the pair given in the last option.
The correct answer is D