Overview
A logarithmic equation contains a logarithm whose argument includes the variable. The standard method is to rewrite it as an equivalent exponential equation and solve that. Always confirm the logarithm argument is positive, since logarithms are undefined for non-positive numbers.
Formula
log_b(ax + c) = d means ax + c = b^d, so x = (b^d − c) ÷ a.
How it works
Check the base
Require b > 0 and b ≠ 1.
Convert to exponential form
Write ax + c = b^d.
Solve for x
Subtract c and divide by a.
Check the domain
Confirm ax + c > 0, then verify the original equation.
Worked examples
Example 1: log₂(x) = 3
x = 2³ = 8.
Example 2: log₂(x + 1) = 4
x + 1 = 16, so x = 15.
Frequently asked questions
Why must the logarithm argument be positive?
The logarithmic function is defined only for positive numbers.
What if the base is 10?
Use log₁₀, or enter 10 as the base in the calculator.
Can a solution be rejected?
Yes. If it makes the logarithm argument non-positive, it must be discarded.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.