How do you evaluate antilog 0.33736?

May 2, 2017

The inverse of a logarithm is exponentiation with its base.

Explanation:

For example the inverse of the base 10 logarithm, (${\log}_{10} \left(x\right)$), is ${10}^{{\log}_{10} \left(x\right)}$ by the definition of any inverse this always gives us x:

${10}^{{\log}_{10} \left(x\right)} = x$

Another example

${2}^{{\log}_{2} \left(x\right)} = x$

Suppose that we have an equation:

${\log}_{3} \left(x - 1\right) = 4$

Make both sides of the equation an exponent of the base, 3:

${3}^{{\log}_{3} \left(x - 1\right)} = {3}^{4}$

The left side becomes the argument within the logarithm, x -1:

$x - 1 = {3}^{4}$

The right side becomes 81:

$x - 1 = 81$

$x = 82$

Another example with base e:

$\ln \left(x + 2\right) = 2$

Make both sides and exponent of the base, e:

${e}^{\ln \left(x + 2\right)} = {e}^{2}$

The left side becomes $x + 2$:

$x + 2 = {e}^{2}$

Subtract 2 from both sides:

$x = {e}^{2} - 2$

I hope that this helps