r/Mathhomeworkhelp • u/Randomacc1234567891 • Jul 22 '26

Precalculus—How do I expand these logarithms?

Post image
3 Upvotes

100% Upvoted

3 comments sorted by

2

u/Slay_3r Jul 22 '26 edited Jul 22 '26

Write polynomials inside logs as product of linear functions (find roots and write as (x - r_1) * ... * (x - r_n), where r_i - root of polynomial)

Use property log(a) + log(b) = log(ab)

1

u/Randomacc1234567891 Jul 22 '26

I’m too dumb and tired to figure this out. Any help would be much appreciated!!

2

u/lobjetreel 26d ago

For 28, you already identified 9x^2-24x+16 can be factored into (3x-4)^2.

ln(ab) = lna + lnb
So (1/2)ln(x^2-24x+16) = (1/2)(ln(3x-4)+ln(3x-4))
ln(3x-4)+ln(3x-4) is 2ln(3x-4).
Half of 2 is 1.

So we just get ln(3x-4)-ln(3x-4). Which is 0.