Question #018b8

Question

969 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-04T15:06:52

$ln (\frac{131072}{9})$ $ln(131072/9)$

We're asked to simplify the expression

$8 ln 2 + 3 ln 8 - 2 ln 3$ $8ln2 + 3ln8 - 2ln3$

We can use one of the properties of logarithms to help us:

$ul(alnb = ln(b^a)$

For the first term:

$color(red)(8)lncolor(green)(2) = ln(color(green)(2)^color(red)(8))$

And similarly for the other two terms:

$= ln(color(green)(2)^color(red)(8)) + ln(color(green)(8)^color(red)(3)) - ln(color(green)(3)^color(red)(2))$

Now, we can use another property:

$ul(lna + lnb = ln(ab)$

and

$ul(lna - lnb = ln(a/b)$

And so we have

$= ln((2^8 * 8^3)/(3^2))$

$= color(blue)(ulbar(|stackrel(" ")(" "ln(131072/9)" ")|)$