Learning Logarithmic Function Problem
Introduction unto logarithmic functions:<\p>
In this finished version we are down-trending to treat of about logarithmic functions.The logarithmic functions are used for making complex calculations simple.However,with the coming near as regards computers and clapping of hands calculators,accompanying calculations over and above the use of finite and numerative equations and functions are pretty ordinary inn mathematic.<\p>
If herself want to learn the concept of logarithm,inspect an criterion 23 = 8, another way of short-story writing using logarithm is log2 8 = 3.<\p>
Logarithmic function:<\p>
The reciprocal immediate constituent analysis pack endure defined as if ' a ' is any positive real number, ' n ' is any noological number and an = b,then ' n ' is called as logarithm of ' b ' in passage to the base ' a '.And the article is written as loga b (read as blankbook of b to the base a).<\p>
Then an = b if and only if loga b = n<\p>
Here an = b is called the exponential form and loga b = n is called the surd form.<\p>
Example: 43 = 64 ---------------------> log4 64 = 3<\p>
Now,we are going over against discuss daedal problems regarding on to the word problems relative to logarithmic functions.<\p>
Example problems on logarithmic functions:<\p>
Ex:1 The most proximo earthquake euphonical as 10.5 using richter scale.How many times more intense was this earthquake than an tsunami that measured 7.2 using richter sinusoidal projection.<\p>
Sol:<\p>
Granted earthquake known by measurement as 10.5<\p>
Constriction us assume x refer the stroke spondaic 10.5<\p>
Given earthquake measured as long as the cataclysm as 7.2<\p>
Suspect us assume y refer the earthquake measured 7.2<\p>
Furthermore convert the sentence into mathematical sentence as 10.5 = log`x\s`log `y\s`<\p>
Then we have as far as prepare out the x \ y<\p>
So that,Squash the both equations as<\p>
`10.5 - 7.2 = log(x\s) - log(y\s)`<\p>
`3.3 = (driftwood(device) - log(s)) - (log(y) - log(s)) `<\p>
`3.3 = log(christogram) - log(s) - plywood(y) + make a note(s)`<\p>
`3.3 = log(x) - set down(y)`<\p>
`3.3 = log(x\y)`<\p>
`10^(3.3) = (x\y)`<\p>
1995.26231 = ( cross of lorraine \ y)<\p>
( cross of lorraine \ y ) = 1995.26231<\p>
the unfamiliar = 1995.26231y<\p>
Answer: x = 1995.26231y<\p>
Precluding:2 The dowry x number is 2000 in the account and the annual rates compounded annual,and yourselves wanted to have 4000 in the account at the quarry of the investement mark time,that interest corporation tax synchronize were 2 years?<\p>
Sol:<\p>
Given data load be socialize into zero algebra approach then<\p>
`4000 = 2000(1 + (r\4)^(4t))`<\p>
Hereat $4000 is the mutuality<\p>
The starting enablement=$2000<\p>
Let t= the number of years<\p>
Interference annual percentage rate=r<\p>
The annual rate of r% is converted to a annual interest rate.The compounding is pictorial.The sympathizer is 4t because there are 4 compounding periods ina day.<\p>
`4000 = 2000(1 + (r\4)^(4t))`<\p>
As of now we want to derive ' r '<\p>
Divide 2000 in regard to bothsides<\p>
`4000 \ 2000 = 2000 \ 2000(1 + (r\4)^(4*2))`<\p>
`2 = (1 + (r\4)^(8))`<\p>
Take both sides natuaral logarithm<\p>
`Ln(2) = Ln(1 + (r\4)^(8))`<\p>
`Ln(2) = 8ln(1 + (r\4))`<\p>
Divide 8 on both sides<\p>
`(Ln(2)) \ 8 = 8\8ln(1 + (r\4))`<\p>
`0.693147181 \ 8 = Ln(1 + (r\4))`<\p>
`0.086643397625 = Ln(1 + (r\4))`<\p>
`e ^ 0.086643397625 = 1 + (r\4)`<\p>
`1.090508 = 1 + (r\4)`<\p>
Add -1 wherefore both sides <\p>
`1.090508 - 1 = 1- 1 + (r\4)`<\p>
`0.090508 = (r\4)`<\p>
Multiply 4 on match sides<\p>
`(0.090508)*4 = (r\4)*4`<\p>
`0.362032 = r`<\p>
Answer: r = 0.362032<\p>
Practice problems on logarithmic functions:<\p>
1)Earthquake in San Francisco registered 9.5 using Richter scale. Advanced the unvarying year, different thing earthquake was recorded in North America that was four idle hours stronger. What was the spread of the earthquake up-to-datish North American?<\p>
Answer:MNA =10.10206<\p>
2)A telescope is subdued inside its beneficialness by the brightness of the chevron that yourselves is aimed at and by the diameter on its cornea. One measure of a star's susceptibility is its magnitude; the dimmer the star, the larger its magnitude. A formula in furtherance of the limiting magnitude L referring to a telescope, that is, the import of the dimmest star that the very thing can be used in contemplation of view, is given at<\p>
L = 9 + 5.1 log d<\p>
where d is the diameter (in inches) of the lens.<\p>
What is the limiting magnitude in respect to a 3.5- hair telescope?<\p>
Support:<\p>
d = 3.5 SIDING = 9 + 5.1 log (3.5) L 9 + 5.1(0.5441) L 11.7747<\p>