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1.5.1 Exponentials and logarithms

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Why is the base restricted to a>0a>0a>0 in axa^xax?

A

For equal positive bases, aman=a^m a^n=aman= am+na^{m+n}am+n and aman=\dfrac{a^m}{a^n}=anam​= am−n\boxed{a^{m-n}}am−n​.

B

A power raised to a power satisfies (am)n=(a^m)^n=(am)n= amn\boxed{a^{mn}}amn​, while a fractional index satisfies a1n=a^{\frac{1}{n}}=an1​= an\sqrt[n]{a}na​.

C

It is increasing from left to right.

D

It ensures axa^xax is real for every real xxx.

Card 1 of 21

1.5.1 Exponentials and logarithms Flashcards

  1. A Level
  2. /Maths
  3. /1.5.1 Exponentials and logarithms

21 flashcards on CCEA A Level Maths 1.5.1 Exponentials and logarithms: the key formulae, methods and definitions you need to recall for AS 1, AS 2, A2 1 and A2 2.

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