Mixed bag

A collection of intriguing questions involving logarithms.
Age
16 to 18
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Here are four exam questions involving logarithms, with the earliest coming from 1966. Can you solve them all?

Question 1

Question 2

Question 3

Question 4