IGCSE Additional Maths Y10: Changing a logarithm to a chosen base — Teach Me

I am a Year 10 pupil taking Cambridge IGCSE Additional Mathematics. Teach me changing a logarithm to a chosen base the way the syllabus presents it, using its command words such as 'show that' and 'hence'. Work one example through step by step, then set me a short question in the same style.