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

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Laws of Logarithms
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Simplify log⁡3(10)+log⁡3(5)\log_3(10) + \log_3(5) using the addition rule.

log⁡3(50)\log_3(50)

What is log⁡a(10)−log⁡a(5)\log_a(10) - \log_a(5) in simplified form?

log⁡a(2)\log_a(2)

Simplify 2log⁡a(6)2\log_a(6) using the power rule.

log⁡a(36)\log_a(36)

What is 12log⁡a(25)+2log⁡a(3)\frac{1}{2}\log_a(25) + 2\log_a(3) simplified?

log⁡a(45)\log_a(45)

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)

Simplify log⁡a(48)−32log⁡a(2)−12log⁡a(9)\log_a(48) - \frac{3}{2}\log_a(2) - \frac{1}{2}\log_a(9).

log⁡a(2)\log_a(2)

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

Combine: log⁡((x−5)/x)=7\log((x-5)/x) = 7

What does log⁡(2)+log⁡(5)\log(2) + \log(5) simplify to?

11

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