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Use the definition of logarithm to simplify each expression.

log 10 ^10
log 10 ^100
log 10 ^ 10-4

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1)\ \ \ log 10 ^(10)=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^(10)\ \ \ \Leftrightarrow\ \ \ \ \ \ x=10\\\\2) \ \ \ log 10 ^(100)=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^(100)\ \ \ \Leftrightarrow\ \ \ x=100\\ \\ 3)\ \ \ log 10 ^ {10-4}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^(10-4)\ \ \ \Leftrightarrow\ \ \ x=6
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