How do you condense $lny+lnt$ ?

Question

1847 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-22T21:03:51

Provided $y, t > 0$ , we have:

$ln y + ln t = ln (yt)$

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:

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

$color(white)()$
So provided $y, t > 0$ we have:

$ln y + ln t = ln (yt)$

How do you condense lny+lntlny+lnt?