Question

Which of the following pairs are equivalent statements?​

Answer 1

Option C.

Explanation:

We need to find the pairs of equivalent statements.

According to the properties of logarithm,

`log_ax=b\Leftrightarrow x=a^b`

Using this property we get

`log_pN=b\Leftrightarrow N=p^b`

Option A is incorrect.

`N^(1/b)=p\Leftrightarrow N=p^b`

Option A is incorrect.

`log_bN=p\Leftrightarrow N=b^p`

Option C is correct.

`log_Nb=p\Leftrightarrow b=N^p\Rightarrow b^{(1)/(p)}=N`

Option D is incorrect.

Therefore, the correct option is C.

Answer 2

`\text{\bf{C.}}\quad\log_b{N}=p\ \text{and}\ b^p=N`

Explanation:

The above answer is basically the definition of the log function. The log function gives you the exponent (p) that results in a number (N) when the base (b) is raised to that power.

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The one thing I try to remember about logarithms is that a logarithm is an exponent.