Flashcards · 10 cards

Logarithms

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Rule
What does $\log_a x = n$ mean?
Answer
$a^n = x$ : the log is the power. So $\log_2 8 = 3$ , because $2^3 = 8$ .
Two ways to say one factThe log is the power
From the lesson: Logarithms and their laws
Rule
The three laws of logarithms?
Answer
$\log xy = \log x + \log y$ , $\log \dfrac xy = \log x - \log y$ and $\log x^n = n\log x$ .
Logs turn × into +On a log scale, lengths add when numbers multiply
From the lesson: Logarithms and their laws
Know it
Is $\log(x + y) = \log x + \log y$ ?
Answer
No. There is no law for the log of a sum. The laws are for the log of a product, a quotient or a power.
From the lesson: Logarithms and their laws
Know it
What are $\log_a a$ and $\log_a 1$ ?
Answer
$\log_a a = 1$ and $\log_a 1 = 0$ . So $\log 10 = 1$ and $\log 100 = 2$ .
From the lesson: Logarithms and their laws
Know it
How do you change the base of a logarithm?
Answer
$\log_a x = \dfrac{\log_b x}{\log_b a}$ .
From the lesson: Logarithms and their laws
Rule
How do you find $\log_{\sqrt2} 8$ without tables?
Answer
Call it $n$ and write it as a power: $(\sqrt2)^n = 8$ , so $2^{\frac n2} = 2^3$ and $n = 6$ .
Call it nIndex form, then the same base on both sides
From the lesson: Logarithms and their laws
Know it
You have solved an equation with logs. What must you check?
Answer
Put each answer back: a log exists only for a positive number. Reject any answer that makes a log undefined.
From the lesson: Logarithms and their laws
Rule
What does $\bar{2}.6754$ mean?
Answer
$-2 + 0.6754 = -1.3246$ . The bar belongs to the characteristic only, so it is not $-2.6754$ .
Bar notation2̄.6754: start at −2, then go forward 0.6754
From the lesson: Using four-figure tables
Know it
What is the characteristic (the whole-number part) of $\log 0.04735$ ?
Answer
$\bar2$ , because $0.04735 = 4.735 \times 10^{-2}$ . From 1 to 10 it is 0; from 10 to 100 it is 1.
From the lesson: Using four-figure tables
Which method?
NECO 2023 · Paper 2 · Q8 (a)
Evaluate without using tables $5\log2 + \log40 - \log12.8$ .
How do you start?
Answer
Move the 5 inside as a power: $5\log 2 = \log 2^5 = \log 32$ . Then combine everything into one log: add for ×, subtract for ÷.
From the lesson: Logarithms and their laws Try the question