CAT Logarithms, indices & surds Questions

Indices describe powers, logarithms reverse exponentiation, and surds retain exact irrational values. These questions rely on applying identities while respecting the domain of each expression.

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Key concepts

• Exponent laws
• Logarithm laws and change of base
• Surd simplification and rationalisation

CAT logarithms, indices & surds practice questions

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Common mistakes

• Splitting the logarithm of a sum into separate logarithms.
• Ignoring that a logarithm needs a positive argument and a positive base other than one.

Practical solving approaches

• Express terms using a common base when possible.
• Keep surds exact and check domain restrictions before cancelling or taking logarithms.

Logarithms, indices & surds FAQs

Is log(a + b) equal to log(a) + log(b)?

No. The addition law applies to a product: log(ab) = log(a) + log(b), with positive arguments and the same valid base.

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CAT Logarithms, indices & surds Questions

Indices describe powers, logarithms reverse exponentiation, and surds retain exact irrational values. These questions rely on applying identities while respecting the domain of each expression.

3 free practice questions

Key concepts

• Exponent laws
• Logarithm laws and change of base
• Surd simplification and rationalisation

CAT logarithms, indices & surds practice questions

Question 1Multiple choiceEASY

Question 1

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Choose an answer

A.

B.

C.

D.

Check answerView solution

Question 2Multiple choiceMEDIUM

Question 2

Select the correct alternative from the given choices

Choose an answer

A.3/2B.1/4C.1/2D.2

Check answerView solution

Question 3Type in the answerMEDIUM

Question 3

Enter your response (as an integer) using the virtual keyboard in the box provided

Your answer

Check answerView solution

Common mistakes

• Splitting the logarithm of a sum into separate logarithms.
• Ignoring that a logarithm needs a positive argument and a positive base other than one.

Practical solving approaches

• Express terms using a common base when possible.
• Keep surds exact and check domain restrictions before cancelling or taking logarithms.

Logarithms, indices & surds FAQs

Is log(a + b) equal to log(a) + log(b)?

No. The addition law applies to a product: log(ab) = log(a) + log(b), with positive arguments and the same valid base.

More Algebra practice

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