SOLUTION: Use the definition of logarithm to simplify each expression. log10 10 log10 1,000 log10 10−4 the -4 is to the -4 power

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Question 940744: Use the definition of logarithm to simplify each expression.
log10 10
log10 1,000
log10 10−4 the -4 is to the -4 power
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Use the definition of logarithm to simplify each expression.
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Comment:: log mean "exponent".
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log10 10 means "the exponent of 10 that gives you 10"
Ans: 1
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log10 1,000 means "the exponent of 10 that gives you 1000"
Ans: 3
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log10 10−4 the -4 is to the -4 power
means "the exponent of 10 that gives you 10^-4
Ans: -4
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cheers
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

simplify each expression: these are common logarithms
Logarithms that use 10 as the base are called common logarithms.
a logarithm answers the question:
How many of one number do we multiply to get another number? The number we are multiplying is called the "base".

log%2810%2C+10%29 here we are asking "how many 10s need to be multiplied together to get 10?" and answer is 1
so, we have log%2810%2C+10%29=1
log%2810%2C+1000%29 "how many 10s need to be multiplied together to get 1000?" and answer is 3 because 10%2A10%2A10=1000 or 10%5E3=1000

so, we have log%2810%2C+1000%29=3
log%2810%2C+10%5E-4%29+
-4%2Alog%2810%2C+10%29+ ...since log%2810%2C+10%29=1
-4%2A1+
-4+
so, log%2810%2C+10%5E-4%29=-4+