Surds, Log and Indices

An interesting question showing these 3 topics can be tested in a single question

Question

Express as

i) Hence show that

ii) Given that , prove that

Techniques tested

• Rationalization
• Indices:
• Power Law:

Answer

Technique used: Rationalization

i)
Techniques used:
Indices:
Power Law:

From LHS

ii)

This part of the question requires us to use the Substitution technique



Using the quadratic formula,

Recall that

therefore

Technique used: Taking log on both sides




Recall that in part (i) we showed that

Interesting question, dont you think ?

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For a revision of surds, click here
For a revision of logarithms, click here
For a revision of indices, click here