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# Log Laws

/Tag: Log Laws
28 11, 2016

## Dividing Logs

Dividing Logs worked examples Simplify $\frac{\log16}{\log8}$.  $=\frac{\log2^4}{\log2^3}$ there is no log law to allow us to directly divide logs, so we are going to rewrite them with the same numbers as powers consider what both 16 and 8 can be written to the power of 16 = 24 and [...]

23 11, 2016

## Logs With Indices

Logs With Indices log ba = a log b worked examples Simplify log 24.  = 4log 2 since log ba  = alog b   we rewrite the log 24 as 4log 2 Rewrite without an index: log x7. = 7log x use the rule log ba  = alog b [...]

9 11, 2016

## Log Expressions

Log Expressions worked examples If x = log10 2, y = log10 8 and z = log10 12, express the following in terms of x, y and z. a. log10 200 b. log10 40 c. log10 32 d. log10 120 a. log10 200 = log10 (2 × 10 × 10) rewrite 200, using only [...]

8 11, 2016

## Log Equations

Log Equations worked examples Solve log3 x = 2. 32 = x change this to the form x = ab, where loga b = x x = 9 calculate Solve log4 (4x - 6) = log4 (2x + 24). 4x - 6 = 2x + 24 since both [...]

25 10, 2016

## Change Of Base

Change Of Base $\log_ab=\frac{\log a}{\log b}$ worked examples Change to log base 10: log3 6 and calculate to 4 decimal places. $\log_36=\frac{\log 6}{\log 3}$ it is convenient for calculating to have the log in base 10, as that is the log button on a calculator. By using the change [...]

25 10, 2016

## Subtracting Logs

Subtracting Logs $\log a - \log b = \log\frac{a}{b}$ worked examples Simplify log 6 - log 3.  = log (6 ÷ 3) since log a - log b = log (a ÷ b), we use this rule to rewrite into a single log = log 2 simplify by calculating 6 ÷ 3 Simplify [...]

24 10, 2016

Adding Logs log a + log b = log (ab) worked examples Simplify log 2 + log 3.  = log (2 × 3) since log a + log b = log ab, we use this rule to rewrite into a single log = log 6 simplify by calculating 2 × [...]

23 10, 2016

## Mixed Log Laws

By |2016-11-28T09:46:58+10:00October 23rd, 2016|Tags: , , , |0 Comments

Mixed Log Laws worked examples Simplify 4log 2 + log 3.  = log 24 + log 3 since alog b = log ba, we rewrite the 4log 2 as log 24 = log (16 × 3) 24 = 16 and the log law for addition is log a + [...]

6 08, 2016

## Simultaneous Log Equations

Simultaneous Log Equations worked examples Solve the pair of simultaneous equations: log10 $\textstyle{x \over y}$ = 2 & log10 x + log10 y = 4. log10 x + log10 y = 4 log10 (xy) = 4  simplify the second equation into a single log, remembering log laws that log [...]