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/Tag: Logs
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 [...]

3 08, 2016

## Simpson’s Rule Logs

By |2016-11-03T09:25:27+10:00August 3rd, 2016||0 Comments

Simpson's Rule Logs worked examples Use Simpson's Rule with three function values to obtain the approximation $\int\limits_1^7 {\left( {\frac{{x - 1}}{6}} \right)} \ln \,x\,\,dx \approx \ln \,\,112$.  $h=\frac{7-1}{2}$ h = 3 values will be 1, 4, 7  find the 3 function values: $h=\frac{b-a}{n}$  where n = number of sub [...]