ffur2007slx2_5
To clarify:
y = 10 ^ x // x = log y
People use logarithm at the purpose of simplifying multiplication via exponents plus years before.
23456*45634 = 1.07039e9
log 23456 = 4.37025; log 45634 = 4.65929; (log 23456) + (log 45634) = 9.02954
10^((log 23456) + (log 45634)) = 10 ^ 9.02954 // same as 23456*45634
As modern usage, for instance, to evaluate another exponent when multiple is known (Which magnitude is 4 times stronger than 8.3 earthquake?):
//_Unknown = log x; 8.3 = log y
// x = 10 ^_Unknown; y = 10 ^8.3
//x/y = (10 ^_Unknown)/(10 ^8.3) = log 4
// x/y = _Unknown – 8.3 = 0.6
//_result = 8.9 magnitude
_result = (log 4) + 8.3