Which of the following pairs are NOT equivalent statements?

In x = y and x = e^y

log⬇️p N = b and b^p = N

x = sqrt y and x = y^1/2

log⬇️b N = p and B^p = N

Answer:

the answer is b

Step-by-step explanation:

bc they are not both equivalent.

The pair (B) is not equivalent after using the property of logarithm option (B) is correct.

It is another way to represent the power of numbers, and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b = c\\log_ac =b[/tex]

It is given that:

The expression is given in the options.

As we know, the expression can be defined as the combination of constants and variables with mathematical operators.

It is required to find the equivalent pairs:

A) In(x) = y and [tex]\rm x = e^y[/tex]

As we know from the log property:

logₙm = a

[tex]\rm \rm n^a = m[/tex]

The pairs are equivalent.

B) [tex]\rm log_p N = b \ and \ b^p = N[/tex]

Again using the log property:

logₙm = a

[tex]\rm \rm n^a = m[/tex]

The pairs are not equivalent.

C) [tex]\rm x = \sqrt y \ and \ x = y^{\dfrac{1}{2}}[/tex]

Using the property of exponent we can write the above expression:

The pairs are equivalent.

D) [tex]\rm log_b N = p \ and \ b^p = N[/tex]

logₙm = a

[tex]\rm \rm n^a = m[/tex]

The pairs are equivalent.

Thus. the pair (B) is not equivalent after using the property of logarithm option (B) is correct.

Learn more about the Logarithm here:

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