# Basic mathematics

log2+3log2-4log7

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1. since sum(logs) = log(product) you have

log(2*2^3/7^4) = log 16/2401

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2. log ( 2 * 2 ^ 3 / 7 ^ 4 ) =

log ( 2 ^ 4 / 7 ^ 4 ) =

log [ ( 2 / 7 ) ^ 4 ] =

4 ∙ [ log ( 2 ) - log ( 7 ) ] =

4 ∙ ( 0.69314718056 - 1.945910149 ) =

4 ∙ ( - 1.25276296845 ) =

- 5.01105187398

OR

log ( 2 * 2 ^ 3 / 7 ^ 4 ) =

log ( 2 * 8 / 2401 ) =

log ( 16 / 2401 ) =

log ( 16 ) - log ( 2401 ) =

2.77258872224 - 7.78364059622 =

- 5.01105187398

In this case:

log is the natural logarithm

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