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NSWMaths AdvancedQuick questions
Year 11: Exponential and Logarithmic Functions
Quick questions on Logarithms and the laws of logarithms for HSC Maths Advanced: a logarithm as the index, converting between index and log form, the product, quotient and power laws, the logs of 1 and of the base, the change-of-base formula, common logarithms base 10, and solving log and index equations
2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What are the three laws of logarithms?Show answer
Because logarithms are indices, the three index laws for combining powers become three laws for combining logarithms of the same base:
What is change of base?Show answer
A calculator's button gives only base (and gives base , the next page's topic). To evaluate a logarithm in any base, the change-of-base formula rewrites it using a base the calculator knows. For bases and ,
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