Question

5) Express as a single logarithm. You do NOT need to expand the polynomials:

5 In(x - 2) + 8 In(x + 3) - 3 ln(x + 8)​

Answer 1

5 ln(x - 2) + 8 ln(x + 3) - 3 ln(x + 8)

ln(x - 2)⁵ + ln(x + 3)⁸ - ln(x + 8)³

since
`a\log_cb=\log_cb^a` (for any base c)

ln((x - 2)⁵ (x + 3)⁸ / (x + 8)³)

since
`\log_c(a)+\log_c(b)=\log_c(ab)` and
`\log_c(a)-\log_c(b)=\log_c\frac ab` (also for any base c)