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# If log10G = 2log10M – log10N, then `G=M^2/N`  .Explain the reason for this.  ...

alejandrogalarce | Student, Undergraduate | Valedictorian

Posted May 22, 2013 at 10:23 AM via web

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If log10G = 2log10M – log10N, then `G=M^2/N`  .Explain the reason for this.

G = M2/N -  why? This is the answer but I am not sure why?

durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted May 22, 2013 at 11:19 AM (Answer #1)

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Logarithms (logs) and exponents (indices) work together just as addition goes with subtraction and multiplication goes with division.

`log_(10)G = 2log_(10)M - log _(10)N` the same as`G=M^2/N`

relates to the rules of logs and exponents such as they relate to each other.

Now also remember that in exponents and logs plus (+) means multiplication and minus(-) means divide.

Therefore `log_(10)M - log_(10)N` is the same as the exponent written as `M/N` because the minus (-) means divide such as we have done by putting M over N.

Everything has the same "base" which is `log_(10)` and the `2log_(10)M` is the same as  `log_(10)M^2`

As the bases are the same we can convert to an exponent :

`log_(10)G= log_(10)M^2 - log_(10)N`

`therefore G = M^2/N`

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