Question 940744

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(10, 10)}}} here we are asking "how many {{{10}}}s need to be multiplied together to get {{{10}}}?" and answer is {{{1}}}

so, we have {{{log(10, 10)=1}}}

{{{log(10, 1000)}}} "how many {{{10}}}s need to be multiplied together to get {{{1000}}}?" and answer is {{{3}}} because {{{10*10*10=1000}}} or {{{10^3=1000}}}


so, we have {{{log(10, 1000)=3}}}

{{{log(10, 10^-4) }}}

{{{-4*log(10, 10) }}} ...since {{{log(10, 10)=1}}}

{{{-4*1 }}}

{{{-4 }}}

so, {{{log(10, 10^-4)=-4 }}}