Exponential equation solver
Match the bases when you can; take a logarithm when you can’t.
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What counts as an exponential equation?
In an exponential equation the variable is in the exponent. If both sides can be written as powers of the same base, set the exponents equal. Otherwise take the logarithm of both sides, which brings the exponent down.
EquationCraft shows the exact logarithm form and a decimal approximation, and graphs both sides so you can see the single crossing point.
How to solve bˣ = k
- Isolate the power (divide off any coefficient, subtract any constant).
- If k is zero or negative, there is no real solution.
- If k is a power of b, rewrite it and set the exponents equal.
- Otherwise take logs: x = log(k) / log(b) (the change-of-base formula).
- Solve the remaining linear equation for x.
Frequently asked questions
Should I use log or ln?
Either one. log(k)/log(b) and ln(k)/ln(b) give the same number. Use ln when the base is e.
Why can’t 2^x equal a negative number?
A positive base raised to any real power is always positive, so the graph of y = 2^x never goes below the x-axis.
What if x appears in two different exponents?
If both can be written with the same base, like 4^x = 2^(x+3), rewrite 4 as 2² and match exponents. EquationCraft’s numeric solver handles the rest by finding where the graphs cross.