Question

Use the properties of log to write each expression as a single log with coficient of 1:

ln(3) -2ln(4) +ln(8)

got this wrong on my quiz and need to figure out how to do for mid-term Please show work..I wrote .41

Answer 1

Here are some of the rules for ln's (natural logarithms)(or logs in general).
log(xy) = log x + log y
log(x/y) = logx - log y
log x^p = p log x

See if you can use them to answer the question...

Answer 2

I'll start u off, using the third rule,

2ln4 = ln 4^2

Answer 3

Ln 3 - 2ln4 + ln 8
=> Ln 3 - Ln (4^2) + Ln 8
=> [Ln3+Ln8] - Ln16
=>Ln(3*8)- Ln 16
=> Ln 24 - Ln 16
=> Ln (24/16)
=> Ln(3/2).. < *Answer*

Answer 4

Right.

http://www.wolframalpha.com/input/?i=ln%283%29+-2ln%284%29+%2Bln%288%29

Answer 5

I deserved a medal there, though! For that elaborate answer! :P