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Logaithm & Anti Logarithm

by tashfeen
(Pakistan)











































LOGARITHMS are a SHORTCUT for EXPONENTS (multiplying and dividing very large and very small numbers).

This simplicity is the reason logarithms are used as the basis for Slide Rules, etc.

plz tell me how could i do logarithm problems?????

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Aug 29, 2011
Logarithm & Anti Logarithm
by: Staff


The question:

by Tashfeen
(Pakistan)


plz tell me how could i do logarithm problems?????



The answer:


This might help to put logarithms in perspective:

MULTIPLICATION is a SHORTCUT for ADDITION (adding the same number over and over): 5 + 5 + 5 + 5 = 4 * 5, four times five

EXPONENTS are a SHORTCUT for MULTIPLICATION (multiplying the same number over and over): 5 * 5 * 5 * 5 = 5⁴, five to the 4th power (the exponent is 4)

LOGARITHMS are a SHORTCUT for EXPONENTS (multiplying and dividing very large and very small numbers).

A logarithm is computed as follows:

if you want to find the logarithm of the NUMBER is 625 using the BASE of 5, then 625 = 5⁴. The LOGARITHM is 4. This can be written: log_5 (625) = log_5 (5⁴) = 4 (the answer is 4 because the exponent is 4).

Using Logs to multiply numbers can be understood using a simple multiplication problem:

(base “n” of each number is the same).

(n²)(n⁶)(n³) = n²⁺⁶⁺³ = n¹¹

The exponent of 11 can also be calculated by adding the logs of all three numbers:

log_n (n²) + log_n (n⁶) + log_n (n³) = 2 + 6 + 3 = 11.

Since we know the BASE is “n”, the ANTILOG is “n¹¹”.

Now let’s apply this to a multiplication/division problem containing very large and very small numbers …. Something like:

1000000 * .0001 / √(10) = ?

Using a base of 10:

Log_10 (1000000 * .0001 / √(10))

= Log_10 (1000000) + Log_10 (.0001) - Log_10 (√(10))

= Log_10 (10⁶) + Log_10 (10⁻⁴) - Log_10 [10^(0.5)]

= 6 + (-4) - 0.5

= 1.5

Since we know the base is 10, the ANTI-LOG is:

= 10^(1.5)

= 31.6228


You have probably already noticed that adding or subtracting logarithms is simple arithmetic [e.g.: 6 + (-4) - 0.5] . . . compared to multiplying large and small numbers using the standard form [e.g.: 1000000 * .0001 / √(10)].

This simplicity is the reason logarithms are used as the basis for Slide Rules, the Richter Scale, the Decibel Scale, etc.



Thanks for writing.

Staff
www.solving-math-problems.com


Sep 03, 2011
THANKS
by: Anonymous

thanks for your this favour.it is very use full for me

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