Using prop of natural logarithms simplify:  f(x)=ln (x/4) + ln4

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mvcdc eNotes educator| Certified Educator

We want to simplify: `ln(x/4) + ln4`

One of the properties of logarithm (in this case natural logarithm, which is just log of base e) states that the logarithm of a product is just the sum of the logarithms:

`log(xy) = log(x) + log(y)`


`ln(xy) = ln(x) + ln(y)`

Hence, since we are dealing with sum of logarithms (lns), we can simply take the product of the values inside them:

`ln(x/4) + ln(4) = ln((x/4)*(4)) =ln((4x)/4) = ln(x)`

Hence, f(x) = ln(x).