nComps = {1, 2, 3, 4, 5};
memory = {76080, 517176, 12750888, 78101640, 1880868104};
data = MapThread[{#1, #2} &, {nComps, memory}];

yTicksMajor =
  Table[{N[10^i], Superscript[10, i], {tickLength, 0},
    Thickness[majorTickThickness]}, {i, 4, 10}];
yTicksMinor =
  Table[{N[j*10^i], "", {tickLengthMinor, 0},
    Thickness[minorTickThickness]}, {i, 4, 10}, {j, 2, 9, 2}];
yTicksTotal =
  Flatten[Table[
    Join[{yTicksMajor[[i]]}, yTicksMinor[[i]]], {i, 1,
     Length@yTicksMajor}], 1];

xTicksMajor =
  Table[{i, i, {tickLength, 0}, Thickness[majorTickThickness]}, {i, 0,
     10}];
xTicksMinor =
  Table[{i + j, "", {tickLengthMinor, 0},
    Thickness[minorTickThickness]}, {i, 0, 10}, {j, 0.2, 1, 0.2}];
xTicksTotal =
  Flatten[Table[
    Join[{xTicksMajor[[i]]}, xTicksMinor[[i]]], {i, 1,
     Length@xTicksMajor}], 1];

ListLogPlot[data, Frame -> True,
 FrameTicks -> {{yTicksTotal, None}, {xTicksTotal, None}},
 ImageSize -> Large]

yTicksTotal = Table[10^i, {i, 5, 10}]