What is logarithm?

what are characteristic and mantissa?

how to find characteristic and mantissa whether we should calculat them from value or by equation?

wahat is the characteristic for 34.263?

what are the characteristic and mantissa for log 5^20?

I need the whole definition

Inmathematics, thelogarithmof anumberis theexponentto which another fixed value, thebase, must be raised to produce that number. For example, the logarithm of1000to base10is3, because10to the power3is1000(as1000 = 10 × 10 × 10 = 103). More precisely, for any two positivereal numbersbandxwherebis not equal to1, the logarithm ofxtobaseb, denotedlogb(x), is the unique real numberysuch that
by=x.