Convert logarithm bases
Change of base: rewrite log_a(x) using ln or any new base.
Also known as: convert logarithm bases calculator, change of base calculator, convert logarithm bases, powers & logs math, powers & logs convert logarithm bases
Inputs
Results update when you click Convert.
log₍10.0000₎(32.0000)
1.505150
log_2.0000(32.0000) = ln(32.0000)/ln(2.0000) = 5.000000
- Original log_2.00005.000000
Ad · below results slot
Recently used
Tools you open will show up here on this device — with your last inputs when available.
What this result means
Change of base: rewrite log_a(x) using ln or any new base. log_a(x) = log_c(x) / log_c(a) = ln(x) / ln(a).
Assumptions
- Rule dependency: Universal formula.
How is it calculated?
log_a(x) = log_c(x) / log_c(a) = ln(x) / ln(a).
Example
log₂(32) = log₁₀(32)/log₁₀(2) = 5.
Frequently asked questions
Why ln?+
Natural log is convenient on calculators; any valid base works.