What is the inverse of a logarithmic function?

Question

What is the inverse of a logarithmic function?

1 Answer

Impact of this question

2017 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-10T12:38:13

The inverse of a logarithmic function is exponential function.

Explanation:

The inverse of a logarithmic function is exponential function:
$\times x f^{- 1} (x) = g^{- 1} (a^{x})$ $color(white)(xxx)f^-1(x)=g^-1(a^x)$
Because logarithmic fuction is
$\times x f (x) = {log}_{a} g (x)$ $color(white)(xxx)f(x)=log_a g(x)$
$\Rightarrow g (x) = a^{f (x)}$ $=>g(x)=a^f(x)$
$\Rightarrow g^{- 1} (g (x)) = g^{- 1} (a^{f (x)})$ $=>g^-1(g(x))=g^-1(a^f(x))$
$\Rightarrow x = g^{- 1} (a^{f (x)})$ $=>x=g^-1(a^f(x))$
$\Rightarrow f^{- 1} (x) = g^{- 1} (a^{x})$ $=>f^-1(x)=g^-1(a^x)$

Considering f(x)=x is axis of symmetry, for $g (x) = x$ $g(x)=x$ and $a = 10$ $a=10$ ,
![ rechneronline.de )

Science

Math

Humanities

... and beyond

What is the inverse of a logarithmic function?

1 Answer

Explanation:

Related questions

Impact of this question