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JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Basics of Mathematics

JEE Main · Mathematics · Basics of Mathematics

aligned & 1+x _e a+(x^2)/(2 !)( _e a)^2 & +(x^3)/(3 !)( _e a)^3+...

\begin{aligned} & 1+x \log _e a+\frac{x^2}{2 !}\left(\log _e a\right)^2 \\ & +\frac{x^3}{3 !}\left(\log _e a\right)^3+\ldots(a>0, x \in R) \text { is equal to }\end{aligned}

Options

A $a$
B $a^x$
C $a^{\log _e x}$
D $x$

Correct answer

B. $a^x$

Step-by-step solution

We have,

\begin{aligned} & 1+x \log _e a+\frac{x^2}{2 !}\left(\log _e a\right)^2+\frac{x^3}{3 !}\left(\log _e a\right)^3+\ldots \\ & =1+\log _e a^x+\frac{1}{2 !}\left(\log _e a^x\right)^2+\frac{1}{3 !}\left(\log _e a^x\right)^3+\ldots \\ & =e^{\log _e a^x}=a^x \end{aligned}

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