How do you condense lny+lnt?

1 Answer
Aug 22, 2017

Provided y, t > 0, we have:

ln y + ln t = ln (yt)

Explanation:

Note that if a, b > 0 then:

ln a + ln b = ln (ab)

This follows from the corresponding property of exponents:

e^(p+q) = e^p * e^q

since e^x and ln x are inverses of one another.

So given a, b > 0, let:

p = ln a" " and " "q = ln b.

Then:

e^p = a" " and " "e^q = b

So:

ln a + ln b = p + q = ln(e^(p+q)) = ln(e^p * e^q) = ln(ab)

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So provided y, t > 0 we have:

ln y + ln t = ln (yt)