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What is `log_( 10) .001` ?

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted August 14, 2013 at 5:13 AM via web

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What is `log_( 10) .001` ?

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted August 14, 2013 at 5:34 AM (Answer #1)

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Here we should know some rules in logarithm.

`log_a(b^n) = nlog_a(b)`

`log_a(a) = 1`

`0.001 = 10^-(3)`

`log_10(0.001)`

`= log_10(10^(-3))`

`= -3log_10(10)`

`= -3(1)`

`= -3`

So the answer is;

`log_10(0.001) = -3`

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