Revise what logarithms are and how to use the 'log' buttons on a scientific calculator
Part ofMathsAlgebraic and trigonometric skills
Now that you know what \({\log _a}x\) means, you should know and be able to use the following results, known as the laws of logarithms.
Thus:
\({\log _{10}}1000 = {\log _{10}}{10^3} = 3{\log _{10}}10 = 3 \times 1 = 3\)
Write \({3^2} = 9\) as a log statement.
\({3^2} = 9 \leftrightarrow {\log _3}9 = 2\)
Write \({\log _5}125 = 3\) as a power statement.
\({\log _5}125 = 3 \leftrightarrow {5^3} = 125\)
Simplify \(5{\log _8}2 + {\log _8}4 - {\log _8}16\)
Method one
\(5{\log _8}2 + {\log _8}4 - {\log _8}16\)
To add the logs, multiply the numbers.
\(= {\log _8}\frac{{{2^5} \times 4}}{{16}}\)
To subtract the logs, divide the numbers.
\(= {\log _8}\frac{{32 \times 4}}{{16}} = {\log _8}8 = 1\)
Method two
\(= 5{\log _8}2 + 2{\log _8}2 - 4{\log _8}2\)
\(= 3{\log _8}2 = {\log _8}{2^3} = {\log _8}8 = 1\)
