1. What Are Exponential Equations?

Exponential equations are equations in which variables appear as exponents. The general form is \( a^x = b \), where \( a \) is the base, \( x \) is the exponent, and \( b \) is the result.

2. How Does the Calculator Work?

The calculator solves equations of the form:

The solution is found using logarithms:

Where:

• \( a \) — Base (must be positive and not equal to 1)
• \( b \) — Result (must be positive)
• \( \ln \) — Natural logarithm

3. Importance of Exponential Equations

Details: Exponential equations are fundamental in many areas including compound interest calculations, population growth models, radioactive decay, and more.

4. Using the Calculator

Tips: Enter positive values for both base (a) and result (b). The base cannot be 1. The calculator will solve for x in the equation \( a^x = b \).

5. Frequently Asked Questions (FAQ)

Q1: What if the base is 1?
A: The equation \( 1^x = b \) only has solutions when b=1 (infinite solutions) or no solution when b≠1.

Q2: Can I use negative numbers?
A: No, the calculator only works with positive real numbers for both base and result.

Q3: What about complex solutions?
A: This calculator only provides real number solutions.

Q4: How accurate are the results?
A: Results are accurate to 4 decimal places.

Q5: Can this solve more complex exponential equations?
A: This calculator only solves basic exponential equations of the form \( a^x = b \).