diff --git a/src/axes.jl b/src/axes.jl
index 0a39576f..8b2836dc 100644
--- a/src/axes.jl
+++ b/src/axes.jl
@@ -172,7 +172,7 @@ function optimal_ticks_and_labels(ticks, alims, scale, formatter)
         scaled_ticks = optimize_ticks(
             sf(amin),
             sf(amax);
-            k_min = scale in _logScales ? 2 : 4, # minimum number of ticks
+            k_min = scale ∈ _logScales ? 2 : 4, # minimum number of ticks
             k_max = 8, # maximum number of ticks
             scale = scale,
         )[1]
@@ -352,23 +352,23 @@ function get_minor_ticks(sp, axis, ticks)
     ticks =  [ticks[1] - first_step/ratio; ticks; ticks[end] + last_step*ratio]
 
     # Default to 9 intervals between major ticks for log10 scale and 5 intervals otherwise.
-    n_default = (scale === :log10) ? 9 : 5
+    n_default = (scale == :log10) ? 9 : 5
     n = typeof(axis[:minorticks]) <: Integer && axis[:minorticks] > 1 ? axis[:minorticks] : n_default
-    is_log_scale = scale in _logScales
-    base = is_log_scale ? _logScaleBases[scale] : nothing
-    sub = is_log_scale ? round(Int, log(ratio) / log(base)) : nothing
+    is_log_scale = scale ∈ _logScales
+    base = get(_logScaleBases, scale, nothing)
+    exp = is_log_scale ? round(Int, log(base, ratio)) : nothing
 
     minorticks = typeof(ticks[1])[]
     for (i, hi) in enumerate(ticks[2:end])
         lo = ticks[i]
         if isfinite(lo) && isfinite(hi) && hi > lo
             if is_log_scale
-                for j in 1:sub
-                    lo_ = lo * base^(j - 1)
+                for e in 1:exp
+                    lo_ = lo * base^(e - 1)
                     hi_ = lo_ * base
                     step = (hi_ - lo_) / n
                     append!(minorticks, collect(
-                        lo_ + (j > 1 ? 0 : step) : step : hi_ - (j < sub ? 0 : step / 2)
+                        lo_ + (e > 1 ? 0 : step) : step : hi_ - (e < exp ? 0 : step / 2)
                     ))
                 end
             else
@@ -512,12 +512,12 @@ end
 # -------------------------------------------------------------------------
 
 # push the limits out slightly
-function widen(lmin, lmax, scale = :identity)
+function widen(lmin, lmax, scale=:identity)
     f, invf = RecipesPipeline.scale_func(scale), RecipesPipeline.inverse_scale_func(scale)
     span = f(lmax) - f(lmin)
     # eps = NaNMath.max(1e-16, min(1e-2span, 1e-10))
     eps = NaNMath.max(1e-16, 0.03span)
-    invf(f(lmin)-eps), invf(f(lmax)+eps)
+    invf(f(lmin) - eps), invf(f(lmax) + eps)
 end
 
 # figure out if widening is a good idea.
@@ -539,10 +539,11 @@ function default_should_widen(axis::Axis)
     false
 end
 
-function round_limits(amin,amax)
-    scale = 10^(1-round(log10(amax - amin)))
-    amin = floor(amin*scale)/scale
-    amax = ceil(amax*scale)/scale
+function round_limits(amin, amax, scale)
+    base = get(_logScaleBases, scale, 10.)
+    factor = base^(1 - round(log(base, amax - amin)))
+    amin = floor(amin * factor) / factor
+    amax = ceil(amax * factor) / factor
     amin, amax
 end
 
@@ -579,7 +580,7 @@ function axis_limits(sp, letter, should_widen = default_should_widen(sp[Symbol(l
         if axis[:letter] == :x
             amin, amax = 0, 2pi
         elseif lims == :auto
-            #widen max radius so ticks dont overlap with theta axis
+            # widen max radius so ticks dont overlap with theta axis
             0, amax + 0.1 * abs(amax - amin)
         else
             amin, amax
@@ -587,12 +588,15 @@ function axis_limits(sp, letter, should_widen = default_should_widen(sp[Symbol(l
     elseif should_widen
         widen(amin, amax, axis[:scale])
     elseif lims == :round
-        round_limits(amin,amax)
+        round_limits(amin, amax, axis[:scale])
     else
         amin, amax
     end
 
-    if !has_user_lims && consider_aspect && letter in (:x, :y) && !(sp[:aspect_ratio] in (:none, :auto) || RecipesPipeline.is3d(:sp))
+    if (
+        !has_user_lims && consider_aspect && letter in (:x, :y) &&
+        !(sp[:aspect_ratio] in (:none, :auto) || RecipesPipeline.is3d(:sp))
+    )
         aspect_ratio = isa(sp[:aspect_ratio], Number) ? sp[:aspect_ratio] : 1
         plot_ratio = height(plotarea(sp)) / width(plotarea(sp))
         dist = amax - amin
@@ -728,6 +732,7 @@ function axis_drawing_info(sp, letter)
             invf = RecipesPipeline.inverse_scale_func(oax[:scale])
 
             add_major_or_minor_segments(ticks, grid, segments, factor, cond) = begin
+                ticks === nothing && return
                 if cond
                     tick_start, tick_stop = if sp[:framestyle] == :origin
                         t = invf(f(0) + factor * (f(oamax) - f(oamin)))
@@ -853,6 +858,7 @@ function axis_drawing_info_3d(sp, letter)
             ga0, ga1 = sp[:framestyle] in (:origin, :zerolines) ? (namin, namax) : (na0, na1)
 
             add_major_or_minor_segments(ticks, grid, segments, factor, cond) = begin
+                ticks === nothing && return
                 if cond
                     tick_start, tick_stop = if sp[:framestyle] == :origin
                         t = invf(f(0) + factor * (f(namax) - f(namin)))