ALG-06

Exponential a^x

y = a^x = e^{x ln a} for a > 0.

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ExponentialExponential

Governing equation

y=a^x

where

a: Base (—)
x: Exponent (—)
y: a^x (—)

Lecture brief

Historical brief

From al-Khwārizmī’s restoration to the quadratic formula, AM–GM, De Moivre and logarithms, algebra is the closed-form skeleton under every lab. These sheets solve, bound and compound. This sheet (ALG-06 — Exponential a^x) is the form associated with Exponential. Working symbols: $a$ , $x$ $\rightarrow$ $y$ . The exponential is the inverse of the logarithm. a^{x+y} = a^x a^y.

Purpose

Purpose: compute

y

from

a

x

in Algebra via

y=a^x

y = a^x = e^{x ln a} for a > 0. Use it when a real algebra question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

a = 2.000\,\mathrm{—}

x = 3.000\,\mathrm{—}

, the governing relation

y=a^x

yields

y = 8.0000\,\mathrm{—}

. Positive base, real exponent. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Base a2 —Exponent x3 —

Outputs

a^x y8.0000 —

Reading speed

Watch on YouTube

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Narration of this film

Positive base, real exponent.

The exponential is the inverse of the logarithm. a^{x+y} = a^x a^y.

Reading speed

Watch on YouTube