Question

The logarithmic form of ax=N is
A) a = logxN B) x = logaN
C) N=logax
D) N=logxa
​

Answer 1

Given :- The logarithmic form of a^x = N is :-

A) a = logxN

B) x = logaN

C) N=logax

D) N=logxa

Solution :-

we know that,

$\bf\: if\:{a}^{n}=x,\\\bf\: then\: ,\\\bf log_{a}(x) = n$

therefore, we can conclude that,

$\rightarrow \: {a}^{x} = n\\\rightarrow \boxed{\bf \: x = log_{a}(n) (b)(ans.)}$

Learn more :-

● $\orange{\bold{Product\:Rule\:Law:}}$

loga (MN) = loga M + loga N

● $\pink{\bold{Quotient\:Rule\:Law:}}$

loga (M/N) = loga M - loga N

● $\green{\bold{Power\:Rule\:Law:}}$

IogaM^(n) = n Ioga M

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The Logarithmic form of

$\sf{ {a}^{x} =N }$

A. $\sf{a = log_{x} N }$

B. $\sf{x = log_{a} N }$

C. $\sf{N = log_{a}x }$

D. $\sf{N = log_{x}a }$

EVALUATION

Here it is given that

$\sf{ {a}^{x} =N }$

Taking logarithm in both sides we get

$\sf{ log( {a}^{x} )= log N }$

$\sf{ \implies \: x log a = log N }$

$\displaystyle \sf{ \implies \: x = \frac{log N}{log a} }$

$\displaystyle \sf{ \implies \: x = log_{a}N }$

FINAL ANSWER

Hence the correct option is

B. $\sf{x = log_{a} N }$

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