How this calculator works
Changing base preserves the logarithm value while expressing it as a quotient. Both component logs use the new base. Choose argument or original base to reverse the relationship. Bases between zero and one work too. Values very close to one can amplify rounding in logarithms.
Formula
log_b(x) = log_c(x)/log_c(b), with x > 0 and b,c > 0, b,c != 1.
Worked example
For log_2(8) in base 4, the numerator is 1.5 and denominator is 0.5. Dividing gives 3, matching 2^3 = 8.
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Frequently asked questions
Does the new base change the answer?
No. It changes the two component logarithms by the same scale factor.
Can I choose a base below one?
Yes, provided it is positive. Both component signs adjust consistently.
Why must the argument be positive?
Real powers of a positive base are positive, so their inverse logarithm has only positive arguments.