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Logarithm for Chemistry Calculations

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                <p>In chemistry especially in kinetics, thermodynamics,
adsorption, photochemistry, electrochemistry, UV, nuclear chemistry,
quantum chemistry, and statistical chemistry etc log is very frequently
used tool to solve calculations. However, for users, applications of
mathematical equation and similar others, unnecessarily cause phobia
about a feeling that log and mathematics are difficult. Since the non-
mathematical background people do not frequently use log and they also do
not pay attention for understanding its simplicity so get unnecessary
fear. This is very simple fundamental of mathematics and saves a lot of
times. For example, number 1000 is depicted as 103Â =Â 1000. For log
form, the number is 1000, the base is 10 on which power is 3. So
log101000Â =Â 3 as log10 =1. So putting log form into original form is as
1x1000Â =Â 103, both the sides the base 10 is maintained. The log of 1000
to base 10 has power or exponent = 3. The reverse operation generates
1000 as number. The 3 is power, this operation is for positive real
numbers.</p>
<p>Let 1000 = x number, and in general, the log of <em>x</em> to base
<em>b</em> is depicted as log<em>b</em>(<em>x</em>), when the base is
implicit then the depictation is as log(<em>x</em>). The exponent y is
raised to the base b as under.</p>
<p>x = by, taking log the same is noted as y = logb(x)</p>
<p>The base 10 is for common use, and <em>e</em> for the natural log and
2 is used for the binary numbers. Keeping same base log its
multiplication as under.</p>
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<p>Log (x.y) = log (x) + log (y), for example, log (4 x 9) = log (4) +
log (9)</p>
<p>The log of the product of two numbers is the sum of the log of those
numbers. Similarly, log reduces division to subtraction by the
formula.</p>
<p>Log (x/y) = log (x) – log (y)</p>
<p>The log of the quotient of two numbers is difference between the logs
of those numbers. Thus the log has applications in diverse fields like
statistics, chemistry, physics, astronomy, computer science, economics,
music, and engineering.</p>
<p><strong>Log of positive real numbers</strong></p>
<p>The log is denoted as bx = y where log x is logb(y), when base
b = 2, then log2(8) = 3. The number 8 is depicted as
23 = 2 x 2 x 2 = 8. So base 2 works well with number 8 and log is
log2(8) = 3. Similarly the number 16 is depicted as
24 = 2 x 2 x 2 x2 = 16, and its log2(16) = 4. Thus with number
the exponent varies.</p>
<p>Interestingly if number is ½ then it could be depicted as 2-1=1/21 =
½. Hence log is log2(1/2) = -1. Similarly if number is ¼ then log is
log2(1/4) = 2-2= 1/22= ¼, hence log2(1/4) = -2.</p>
<p>Similarly the log2(3) ≈ 1.58.</p>
<p><strong>Logarithm of a product</strong></p>
<p>The log3(9 x 27) = log3(243) = 5 due to 35 = 243. Also the sum of
log3(9) = 2 and log3(27) = 3 also equals 5. Basically, the log defines
contributory variables of individual parameter of certain operation
executed on specific materials like aqueous mixtures of proteins,
polymers, amino acids, dendrimeres, binary, ternary, ionic or molecular
mixtures. For example, the Friccohesity depends on viscous flow time t
and pendant drop number n. The t and n are contributory variables to the
friccohesity for constant liquid volume filled in, in Survismeter
functional bulb is taken as base. Thus, the friccohesity could be
depicted as logV(t x n) where frictional and cohesive forces do
contribute a lot.</p>
<p><strong>Log of a power</strong></p>
<p>The same is noted as logb(xp) = p logb(x), example, log2(64) =
log2(43) = 3 log2(4) = 3 x 2 = 6. Thus x number is generated as x =
blogb(x) and xp = (blogb(x))p = bp · logb(x).</p>
<p>The (de)f = de · f, where d, e and f are positive real numbers. Thus,
the logb of the left hand side, logb(xp), and of the right hand side, p
· logb(x), agree.</p>
<p><strong>Change of base</strong></p>
<p>The ba = x, thus the logk(x) = logk(ba) = a  logk(b).</p>
<p>The general restriction b ≠1 implies logkb ≠0, since b0 = 1.</p>
<p><strong>Natural log</strong> is log to base e, the e is an irrational
constant and equal to 2.7183. The natural log is noted as ln(x) or
loge(x), when base e is implicit then as log(x). The natural log of x is
ln(x)). Here the power to which e would have to be raised to equal x. For
example, ln(7.389) is 2, because e2=7.389. The natural log of e itself
(ln(e)) = 1 as e1 = e while the natural log of 1 (ln(1))=0 because the e0
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