Expert: Steve Holleran - 9/25/2007

Question
ok so here goes. i need help with writing this as a single logarithm.   logb 4+3[logb(1+x)-logb(1-x)]

Answer
Hi Kyle,

Okay, first, I'm going to leave out all the "b"s that are just subscripts.  You can put it back in at the end, okay?

Let's do this in steps:

log 4 + 3[log(1+x) - log(1-x)]

= log 4 + 3[log ((1+x)/(1-x))]

= log 4 + log[((1+x)/(1-x))]^3

= log 4[((1+x)/(1-x))]^3

These steps are all from the 3 main properties of logarithms.  They are probably listed prominently somewhere in your text.

Hope this helps
Steve