Question

Logarithms and Their Properties?

Answer 1

`log 0.001 root (5)p=-3+1/5n`
`log(0.00001times p^6/q^7)=-5+6n+7m`

Explanation:

If you just have plain "log", it means log base 10 ie `log_10`

`log 0.001 root (5)p`

Remember: `log ab=log a + log b`
=`log 0.001 + log root(5)p`

=`log 10^(-3)+log p^(1/5)`

Remember: `log_a a=1` and `log_a b^n=n log_a b` where n is a number
=`-3+1/5log p`

=`-3+1/5n`

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`log(0.00001times p^6/q^7)`

Remember: `log a/b= log a - log b`
=`log 0.00001 + log p^6 + log q^7`

=`log 10^(-5) + log p^6 + log q^7`

=`-5+6log p+ 7 log q`

=`-5+6n+7m`