If we plot the distributions, we observe that they cannot have arisen from a log transformation, because there are no values near 0, which would represent unity in a log transformation and is where we would expect most of the data to fall:

df %>%
  select(starts_with("Fold")) %>%
  gather(key, value) %>%
  ggplot(aes(value, color=key)) +
    geom_density(n=4096) +
    coord_cartesian(xlim=c(-5, 5)) +
    guides(color="none")

In fact… are any values -1 < x < 1?

df %>%
  select(starts_with("Fold")) %>%
  gather(key, value) %>%
  filter(value < 1, value > -1) %>%
  nrow

## [1] 0

So that’s a no.

Also, the range is somewhat greater than -5, 5:

df %>%
  select(starts_with("Fold")) %>%
  gather(key, value) %>%
  group_by(key) %>%
  summarize(min=min(value), max=max(value)) %>%
  knitr::kable()

key	min	max
Fold-Change(baseline vs. GC)	-12.22470	13.65620
Fold-Change(baseline vs. HDL)	-2.90123	2.22134
Fold-Change(baseline vs. IFNb)	-8.60802	2.58496
Fold-Change(baseline vs. IFNg_TNF)	-43.08150	42.17510
Fold-Change(baseline vs. IFNg)	-34.30280	10.25130
Fold-Change(baseline vs. IL10)	-4.49985	6.08848
Fold-Change(baseline vs. IL13)	-38.88690	21.85800
Fold-Change(baseline vs. IL4_upLPS)	-37.23170	9.86970
Fold-Change(baseline vs. IL4)	-30.06650	16.26230
Fold-Change(baseline vs. LA)	-22.92680	11.23740
Fold-Change(baseline vs. LiA)	-29.10950	13.60780
Fold-Change(baseline vs. OA)	-42.07400	10.46060
Fold-Change(baseline vs. P3C_PGE2)	-113.15200	6.67239
Fold-Change(baseline vs. P3C)	-12.13370	5.62230
Fold-Change(baseline vs. PA)	-27.37880	17.37790
Fold-Change(baseline vs. PGE2)	-42.43130	6.28818
Fold-Change(baseline vs. SA)	-32.21920	13.58090
Fold-Change(baseline vs. sLPS_IC)	-29.75090	18.98120
Fold-Change(baseline vs. sLPS_IFNg)	-72.52780	49.97010
Fold-Change(baseline vs. sLPS)	-38.95170	20.89660
Fold-Change(baseline vs. TNF_P3C)	-22.70020	9.19451
Fold-Change(baseline vs. TNF_PGE2)	-36.85690	14.10300
Fold-Change(baseline vs. TNF)	-28.13700	25.34570
Fold-Change(baseline vs. TPP_IFNb_IFNg)	-65.32070	49.69360
Fold-Change(baseline vs. TPP_IFNb)	-57.88370	32.16020
Fold-Change(baseline vs. TPP)	-34.85550	15.07780
Fold-Change(baseline vs. upLPS_IC)	-16.73070	28.79890
Fold-Change(baseline vs. upLPS)	-8.75729	4.55696