Question

Example 3: Find the number whose logarithm is -2.4678.​

Answer 1

The logarithm is an inverse function of an exponential function.

So we can find the relation between logarithm and exponential.

$\boxed{\sf{y=f(x)}\leftrightarrow x=f^{-1}(y)}$

Let $\sf{f(x)=e^x}$

Then $\sf{f^{-1}(x)=ln\:x}$

Let the complex number be y.

$\sf{ln\:y=-2.4678}$

$\sf{\implies f^{-1}(y)=-2.4678}$

$\boxed{\sf{y=f(x)}\leftrightarrow \underline{\bold{x=f^{-1}(y)}}}$

$\sf{\implies y=f(-2.4678)}$

$\sf{\implies y=e^{-2.4678}}$

$\bold{\therefore y=\dfrac{1}{e^{2.4678}} }}$