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 \( a \lt 0 \).

\( a \) =

Number of Decimal Places =

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 \( b = 1 \).

\( a \) =
\( b \) =

Number of Decimal Places =

Results


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