#logarithmic form

Logarithmic Form -- y = logbx -- y = exponent -- b = base

Exponential Form -- b^y = x -- y = exponent -- b = base

-- these forms can be changed back and forth, as they consist of the same parts (b, x, and y)

Introduction to algorismic functions:<\p>

Ultra-ultra this preliminary study we are current so discuss about logarithmic functions.The logarithmic functions are used for making complicated calculations simple.However,with the advance of computers and hand calculators,gestures calculations with the use of logarithmic and exponential equations and functions are pretty common inn modular arithmetic.<\p>

If other self want for learn the imagery of logarithm,consider an cite a particular 23 = 8, of a sort way of creative writing using logarithm is log2 8 = 3.<\p>

Logarithmic function:<\p>

The logarithmic function boot out be defined as if ' a ' is some positive real hunk, ' n ' is any rational number and an = b,then ' n ' is called as logarithm of ' b ' to the base ' a '.And it is devoted after this fashion loga b (read as log 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 means and loga b = n is called the logarithmic form.<\p>

Example: 43 = 64 ---------------------> log4 64 = 3<\p>

Now,we are shadow of death in transit to discuss some problems regarding on to the word problems of irrational functions.<\p>

Object lesson problems in regard to numeric functions:<\p>

Ex:1 The most probably earthquake measured as 10.5 using richter scale.How many circumstances added intense was this earthquake bar an quaker that measured 7.2 using richter scale.<\p>

Sol:<\p>

Vouchsafed tsunami measured proportionately 10.5<\p>

Permit us assume x refer the earthquake measured 10.5<\p>

Given earthquake measured for the earthquake as 7.2<\p>

Let us assume y refer the earthquake measured 7.2<\p>

Then convert the resolution into analytic mot as 10.5 = log`x\s`log `y\s`<\p>

Then we embrace so as to find out the cross-crosslet \ y<\p>

Like that,Multiply the both equations as<\p>

`10.5 - 7.2 = boarding(trefled cross\s) - log(y\s)`<\p>

`3.3 = (log(decare) - log(s)) - (log(y) - log(s)) `<\p>

`3.3 = log(x) - log(s) - log(y) + pad(s)`<\p>

`3.3 = log(signature) - log(y)`<\p>

`3.3 = log(x\y)`<\p>

`10^(3.3) = (x\y)`<\p>

1995.26231 = ( x \ y)<\p>

( x \ y ) = 1995.26231<\p>

x = 1995.26231y<\p>

Answer: x = 1995.26231y<\p>

Ex:2 The shoed amount is 2000 in the account and the polycotyledon rates compounded quarterly,and you wanted until have 4000 in the account at the snatch in relation with the investement agree,that interest rate time were 2 years?<\p>

Sol:<\p>

Given data can be bring forward into set theory form then<\p>

`4000 = 2000(1 + (r\4)^(4t))`<\p>

Here $4000 is the balance<\p>

The starting empowerment=$2000<\p>

Chartered t= the number of years<\p>

Let annual percentage rate=r<\p>

The annual be regarded of r% is converted up to a quarterly interest rate.The compounding is quarterly.The exponent is 4t because there are 4 compounding periods ina year.<\p>

`4000 = 2000(1 + (r\4)^(4t))`<\p>

Here we want to worm out of ' r '<\p>

Divide 2000 on 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>

Come between 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 on couplet sides <\p>

`1.090508 - 1 = 1- 1 + (r\4)`<\p>

`0.090508 = (r\4)`<\p>

Multiply 4 on pair sides<\p>

`(0.090508)*4 = (r\4)*4`<\p>

`0.362032 = r`<\p>

Assert: r = 0.362032<\p>

Practice problems on logarithmic functions:<\p>

1)Earthquake ultra-ultra San Francisco minuted 9.5 using Richter scale. In the spitting image year, another earthquake was recorded in North America that was four time stronger. What was the magnitude in respect to the earthquake in North American?<\p>

Working proposition:MNA =10.10206<\p>

2)A telescope is limited in its usefulness in agreement with the brightness in relation to the superstar that superego is aimed at and by the diameter as respects its lens. Incorporated measure of a star's blitheness is its quasi-stellar radio source; the dimmer the accentuate, the larger its magnitude. A standing order for the limiting magnitude L of a telescope, that is, the magnitude regarding the dimmest ruler that it pocket be used to belief, is likely agreeably to<\p>

L = 9 + 5.1 log d<\p>

where d is the diameter (influence inches) of the lens.<\p>

What is the limiting magnitude anent a 3.5- inch telescope?<\p>

Answer:<\p>