Question

Use the definition of logarithm to simplify each expression.

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

Answer 1

`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`