Antilogarithm Function is Exponential Function

Theorem

Let $y = \operatorname {alog}_b x$ be the antilogarithm of $x$ base $b$.

Then:

$y = b^x$

Proof

\(\ds y\)

\(=\)

\(\ds \operatorname {alog}_b x\)

by hypothesis

\(\ds \leadsto \ \ \)

\(\ds x\)

\(=\)

\(\ds \log_b y\)

Definition of Antilogarithm

\(\ds \leadsto \ \ \)

\(\ds b^x\)

\(=\)

\(\ds y\)

Definition of General Logarithm

$\blacksquare$

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): antilogarithm
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): antilogarithm