Question

Which of the following is not an equivalent statement for the exponential form $a^x=N$

• A. $x=\sqrt[a]{aN}$
• B. ${\log }_{a}N=x$
• C. $a=\sqrt[x]{xN}$
• D. ${\log }_{x}N=a$

Answer 1

Answer: (A), (D)

$x=\sqrt[a]{aN}$
${\log }_{x}N=a$

Given $a^x=N$

Taking $\log$ we get

${\log }_{a}N=x$

By logarithmic property,

$N=a^x$

Now taking $xth$ root of the given equation

$a=\sqrt[x]{xN}$

So, Option A and D are not an equivalent statement for the exponential form $a^x=N$