pls help pls pls ): precalc

[tex]\log_p N = b[/tex] is not the same as [tex]b^p = N[/tex]
The base of the log is p, while the base of the exponential is b. The two don't match. If it said [tex]\log_p N = b \text{ is the same as } p^b = N[/tex] then it would be a valid statement since the bases are both p.
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Extra info:
Choice B is a valid statement because Ln is a natural log with base 'e'
Choice C is valid as any square root is really something to the 1/2 power
Choice D is valid for similar reasons mentioned earlier
Answer:
A.
Step-by-step explanation:
A is incorrect. The definition of logarithms is that if [tex]log_{a}b=c[/tex], then [tex]a^c=b[/tex].
The variables are in the wrong place. The correct answer should be:
[tex]log_{p}N=b, p^b=N[/tex]
B is correct since as [tex]ln(x)=log_{e}(x)[/tex]. Thus, [tex]e^y=x[/tex]
C is correct because the square root of anything is simply that thing to the one-half power.
D is also correct as this is the definition of a logarithm.