proof concept

main.py

import sys
from random import randint

from PyQt5 import QtCore, QtGui, QtWidgets, QtChart


class Widget(QtWidgets.QMainWindow):
    def __init__(self, parent=None):
        super(Widget, self).__init__(parent)

        series = QtChart.QLineSeries()
        for i in range(10):
            series << QtCore.QPointF(i, randint(3, 5)**i)

        chart = QtChart.QChart()
        chart.addSeries(series)

        axisX = QtChart.QValueAxis()
        axisX.setTitleText("Data point")
        axisX.setLabelFormat("%i")
        axisX.setTickCount(series.count())
        chart.addAxis(axisX, QtCore.Qt.AlignBottom)
        series.attachAxis(axisX)

        axisY = QtChart.QLogValueAxis()
        axisY.setTitleText("Values")
        axisY.setLabelFormat("%g")
        axisY.setBase(8.0)
        axisY.setMinorTickCount(-1)
        chart.addAxis(axisY, QtCore.Qt.AlignLeft)
        series.attachAxis(axisY)

        chartview = QtChart.QChartView(chart)

        self.setCentralWidget(chartview)

        QtWidgets.QShortcut(QtGui.QKeySequence.ZoomOut, self, activated=chart.zoomOut)
        QtWidgets.QShortcut(QtGui.QKeySequence.ZoomIn, self, activated=chart.zoomIn)


if __name__ == '__main__':
    import sys

    app = QtWidgets.QApplication(sys.argv)
    w = Widget()
    w.resize(640, 480)
    w.show()
    sys.exit(app.exec_())