Laws of Logarithms (AQA A-Level Mathematics): Quizzes

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Laws of Logarithms
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What is log⁡(a)+log⁡(b)\log(a) + \log(b) equal to?

log⁡(ab)\log(ab)

Simplify log⁡a(10)−log⁡a(5)\log_a(10) - \log_a(5).

log⁡a(2)\log_a(2)

What does 3log⁡(x)3\log(x) simplify to?

log⁡(x3)\log(x^3)

Simplify 2log⁡a(6)2\log_a(6) in the form log⁡an\log_a n.

log⁡a(36)\log_a(36)

Express log⁡(3a2b3)\log(3a^2b^3) as a sum with no indices.

log⁡(3)+2log⁡(a)+3log⁡(b)\log(3)+2\log(a)+3\log(b)

Simplify 1+log⁡3(5)1 + \log_3(5) as a single logarithm.

log⁡3(15)\log_3(15)

If log⁡ax=p\log_a x = p and log⁡ay=q\log_a y = q, what is log⁡a(xy)\log_a(xy)?

p+qp + q

What is log⁡(2)+log⁡(5)\log(2) + \log(5) equal to?

11

What is the first step to solve log⁡(x−5)−log⁡(x)=7\log(x-5) - \log(x) = 7?

Combine: log⁡(x−5x)=7\log\left(\frac{x-5}{x}\right)=7

Simplify 12log⁡(9)+3log⁡(2)\frac{1}{2}\log(9) + 3\log(2).

log⁡(24)\log(24)

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