# Exponential Equations Solver

Two online calculators and solvers for exponential equations of the form \( b^x = a \) are presented.

We consider two cases:

1) Equations of the form \[ e^x = a \] with base \( b = e \)

whose solution is given by

\[ x = \ln a \quad \text{for} \; a \gt 0 \]
\[\text{No real solutions for} \; a \le 0 \]

2) Equations of the form \[ b^x = a \] with any base \( b \gt 0 \) , \( b \ne 1 \)

whose solution is given by

\[ x = \dfrac{\ln a}{\ln b} \quad \text{for} \; a \gt 0 \text { and } b \ne 1\]
\[\text{No real solutions for} \; a \le 0 \text { or } b = 1 \]

## Use the calculator to solve the equation \( e^x = a \) for \( x \)

Enter \( a \), as a real number, and press "enter". There are no real solutions for \( a \lt 0 \).

## Results

## Use the calculator to solve the equation \( b^x = a \) for \( x \)

Enter \( a \) , and \( b \) as real numbers, and press "enter". There are no real solutions for \( a \lt 0 \) and/or \( b = 1 \).

## Results

More Math Calculators and Solvers .