R - boxplot log scale problem with 0 values - r

Question

I have a dataset that consists of 0 values. I want to use log scale but because of the 0 values, it is returning an error. I tried to replace 0s with 1s and it returned something that did not seem right.
As you can see in the figure, I have very small values for the 16k case but to show it clearly, I want to use log scale. Also, I want the order to be 8k_B, 8k_S, 16k_B, 16k_S. I tried factor and levels but still it didn't change the order.
Can someone please help? I can post the data if necessary. Thank you.
Here is the code I used.
data_freq <- data.frame(name=c( rep("8K_B",24), rep("8K_S",24), rep("16_B",24), rep("16K_S",24)),sines=c(rep("B",24),rep("S",24),rep("B",24),rep("S",24)),
value_freq=c( r1B$Frequency, r1S$Frequency, r2B$Frequency, r2S$Frequency)
)
p <- ggplot(data_freq, aes(x=name, y=value_freq, fill=name)) +
geom_boxplot()
Here is the data:
data_freq <- structure(list(name = structure(c(3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L,
4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("16K_S", "16_B",
"8K_B", "8K_S"), class = "factor"), sines = structure(c(1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("B",
"S"), class = "factor"), value_freq = c(6.269822e-05, 5.494403e-05,
5.84888e-05, 5.727028e-05, 7.300023e-05, 6.502448e-05, 6.568913e-05,
5.771338e-05, 5.638409e-05, 5.693796e-05, 5.527635e-05, 6.103661e-05,
5.660564e-05, 6.269822e-05, 5.594099e-05, 6.978778e-05, 5.571945e-05,
6.258745e-05, 6.779384e-05, 6.668609e-05, 6.048274e-05, 5.826725e-05,
5.671641e-05, 6.070429e-05, 9.433902e-05, 8.037108e-05, 8.203393e-05,
8.591391e-05, 9.633444e-05, 9.123503e-05, 8.946133e-05, 8.447278e-05,
7.638024e-05, 8.103622e-05, 8.15905e-05, 8.480535e-05, 7.527167e-05,
8.779847e-05, 8.192307e-05, 9.7443e-05, 7.649109e-05, 8.425106e-05,
9.134589e-05, 9.555844e-05, 8.724419e-05, 7.881908e-05, 7.771052e-05,
8.358592e-05, 1.1077e-07, 1.1077e-07, 0, 0, 1.1077e-07, 0, 0,
1.1077e-07, 1.1077e-07, 0, 0, 0, 0, 0, 3.3232e-07, 0, 2.2155e-07,
4.431e-07, 1.1077e-07, 1.1077e-07, 1.1077e-07, 0, 2.2155e-07,
0, 5.5428e-07, 5.5428e-07, 6.6514e-07, 6.6514e-07, 7.64911e-06,
6.6514e-07, 6.6514e-07, 1.1086e-07, 5.5428e-07, 6.6514e-07, 6.6514e-07,
6.6514e-07, 3.3257e-07, 6.6514e-07, 0, 6.6514e-07, 3.87998e-06,
6.6514e-06, 1.1086e-07, 1.1086e-07, 1.1086e-07, 3.3257e-07, 3.3257e-07,
1.10857e-06)), class = "data.frame", row.names = c(NA, -96L))

Answer 1

You could try to do log(x+n) transformation instead.
p <- data_freq %>%
mutate(value_freq = log(value_freq + 0.000001)) %>% # your numbers are really small so I am adding a small number
ggplot(aes(x=name, y=value_freq, fill=name)) +
geom_boxplot()
Alternatively, you can try square root transformation.
p <- data_freq %>%
mutate(value_freq = value_freq^(1/2)) %>%
ggplot(aes(x=name, y=value_freq, fill=name)) +
geom_boxplot()
Or do the transformation using ggplot:
p <- data_freq %>%
ggplot(aes(x=name, y=value_freq, fill=name)) +
geom_boxplot() +
scale_y_log10()