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

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Exponential Equations
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What is the first step when solving 5x=2.85^x = 2.8?

Take logs of both sides

Which rule is used to solve log⁡(5x)=log⁡(2.8)\log(5^x) = \log(2.8)?

log⁡(ab)=blog⁡(a)\log(a^b) = b\log(a)

Does using ln⁡\ln instead of log⁡\log change the answer when solving 5x=2.85^x = 2.8?

No, same answer

What does log⁡3(32.173)\log_3(3^{2.173}) equal?

2.1732.173

What does 6log⁡6(0.32)6^{\log_6(0.32)} equal?

0.320.32

To solve log⁡6(x)=0.2\log_6(x) = 0.2, what should you do?

Raise 6 to both sides

What is the first step to solve log⁡(x)+2log⁡(x)=4\log(x) + 2\log(x) = 4?

Combine into log⁡(x3)=4\log(x^3) = 4

For log⁡(x)+2log⁡(x)=4\log(x) + 2\log(x) = 4, why not write 10log⁡(x)+102log⁡(x)=10410^{\log(x)} + 10^{2\log(x)} = 10^4?

1+2=31 + 2 = 3 but 101+102≠10310^1 + 10^2 \neq 10^3

In solving x2−9x−10=0x^2 - 9x - 10 = 0 from a log equation, why reject x=−1x = -1?

Logarithms of negatives don't exist

What is xx in 2x−3=7.22^{x-3} = 7.2 (to 3sf)?

5.855.85

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