Using Excel 2010 the chart tools doesn't show the layout

Sounds like xl2013 or newer.

On the format tab there is a dropdown to select elements of the chart. You can select axis and then Format selection.
Also you should be able to double click the axis in order to display the format task pane.
Another way is to select the chart and use the + button that appears on the right to select element and display format task pane.

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