[Verse 1] When bases meet with powers high Same letters dance, exponents fly a to the m times a to the n Add those powers, here's the blend Multiplication turns to sum The magic trick has just begun [Chorus] Exponents build, logarithms break it down Turn the mountains into level ground What goes up in powers of ten Logs bring back to where we've been Addition, multiplication - they translate Inverse partners, never late [Verse 2] Power raised to another power Multiply those digits, feel the tower a to the zero equals one No matter what the base has done Negative powers flip the script One over a to the n, well-equipped [Chorus] Exponents build, logarithms break it down Turn the mountains into level ground What goes up in powers of ten Logs bring back to where we've been Addition, multiplication - they translate Inverse partners, never late [Bridge] Log of products breaks apart Sum of logs, that's just the start Log of powers pulls them out Multiply what it's about Change of base with natural ln Divide and conquer once again [Verse 3] From starlight distances so vast To pH levels, small and fast Logarithms compress the scale Make enormous numbers pale e appears where growth is pure Natural base, the cure for sure [Chorus] Exponents build, logarithms break it down Turn the mountains into level ground What goes up in powers of ten Logs bring back to where we've been Addition, multiplication - they translate Inverse partners, never late [Outro] Two worlds connected by this bridge Additive and multiplicative ridge Before calculators came to be Logs unlocked complexity
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