# 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 $a \lt 0$.

 $a$ = 2 Number of Decimal Places = 5

## 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 $b = 1$.

 $a$ = 5 $b$ = 3 Number of Decimal Places = 5

## Results

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