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# Log Laws

/Tag: Log Laws
28 11, 2016

## Dividing Logs

By |2016-11-28T09:32:05+10:00November 28th, 2016||0 Comments

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

By |2016-11-28T09:44:16+10:00November 23rd, 2016||0 Comments

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

By |2016-11-28T09:53:46+10:00November 9th, 2016||0 Comments

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

By |2016-11-28T09:06:06+10:00November 8th, 2016||0 Comments

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

By |2016-10-25T10:22:13+10:00October 25th, 2016||0 Comments

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

By |2016-11-28T09:36:10+10:00October 25th, 2016||0 Comments

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

By |2016-11-28T09:34:18+10:00October 24th, 2016||0 Comments

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

By |2016-11-03T08:52:44+10:00August 6th, 2016||0 Comments

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 [...]

17 06, 2016

## Logs

By |2016-11-28T09:29:25+10:00June 17th, 2016|Tags: , , , |0 Comments

Logs Go to the Logs Forum to see more questions or ask your own Topics Covered in Logs Adding Logs Subtracting Logs Logs With Indices Mixed Log Laws Dividing Logs Log Expressions Change Of Base Log Equations [...]