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Enter the mathematical formula directly and click the "Next" button to get the calculation answer.
It supports mathematical functions (including trigonometric functions).
Current location：Mathematical operation > History of Mathematical Computation > Answer
Overview: 1 questions will be solved this time.Among them
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 0.5*ln0.5+0.2*ln0.2+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02 .
Question type: Mathematical calculation
Solution:
0.5*ln0.5+0.2*ln0.2+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*ln0.2+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*-1.89712+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*-1.89712+0.08*-2.525729+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*-1.89712+0.08*-2.525729+0.03*-3.506558+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*-1.89712+0.08*-2.525729+0.03*-3.506558+2*0.02*-3.912023
=-0.346573+0.2*(-1.609438)+0.15*(-1.89712)+0.08*(-2.525729)+0.03*(-3.506558)+2*0.02*(-3.912023)
=-0.346573+(-0.321888)+0.15*(-1.89712)+0.08*(-2.525729)+0.03*(-3.506558)+2*0.02*(-3.912023)
=-0.346573+-0.321888+(-0.284568)+0.08*(-2.525729)+0.03*(-3.506558)+2*0.02*(-3.912023)
=-0.346573+-0.321888+-0.284568+(-0.202058)+0.03*(-3.506558)+2*0.02*(-3.912023)
=-0.346573+-0.321888+-0.284568+(-0.202058)+(-0.105197)+2*0.02*(-3.912023)
=-0.346573+-0.321888+-0.284568+(-0.202058)+-0.105197+0.04*(-3.912023)
=-0.346573+-0.321888+-0.284568+(-0.202058)+-0.105197+(-0.156481)
=-0.668461+(-0.284568)+(-0.202058)+(-0.105197)+(-0.156481)
=-0.953029+(-0.202058)+(-0.105197)+(-0.156481)
=-1.155087+(-0.105197)+(-0.156481)
=-1.260284+(-0.156481)
=-1.416765
Answer:0.5*ln0.5+0.2*ln0.2+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02=-1.416765
☆1 arithmetic calculations
[1/1 Formula]
Work: Calculate the value of equation 0.5*ln0.5+0.2*ln0.2+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02 .
Question type: Mathematical calculation
Solution:
0.5*ln0.5+0.2*ln0.2+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*ln0.2+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*-1.89712+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*-1.89712+0.08*-2.525729+0.03*ln0.03+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*-1.89712+0.08*-2.525729+0.03*-3.506558+2*0.02*ln0.02
=0.5*-0.693147+0.2*-1.609438+0.15*-1.89712+0.08*-2.525729+0.03*-3.506558+2*0.02*-3.912023
=-0.346573+0.2*(-1.609438)+0.15*(-1.89712)+0.08*(-2.525729)+0.03*(-3.506558)+2*0.02*(-3.912023)
=-0.346573+(-0.321888)+0.15*(-1.89712)+0.08*(-2.525729)+0.03*(-3.506558)+2*0.02*(-3.912023)
=-0.346573+-0.321888+(-0.284568)+0.08*(-2.525729)+0.03*(-3.506558)+2*0.02*(-3.912023)
=-0.346573+-0.321888+-0.284568+(-0.202058)+0.03*(-3.506558)+2*0.02*(-3.912023)
=-0.346573+-0.321888+-0.284568+(-0.202058)+(-0.105197)+2*0.02*(-3.912023)
=-0.346573+-0.321888+-0.284568+(-0.202058)+-0.105197+0.04*(-3.912023)
=-0.346573+-0.321888+-0.284568+(-0.202058)+-0.105197+(-0.156481)
=-0.668461+(-0.284568)+(-0.202058)+(-0.105197)+(-0.156481)
=-0.953029+(-0.202058)+(-0.105197)+(-0.156481)
=-1.155087+(-0.105197)+(-0.156481)
=-1.260284+(-0.156481)
=-1.416765
Answer:0.5*ln0.5+0.2*ln0.2+0.15*ln0.15+0.08*ln0.08+0.03*ln0.03+2*0.02*ln0.02=-1.416765