subject: Solve Logarithms Algebraically [print this page] This article will help you to solve logarithms algebraically.
The logarithm of a variety is the exponent by which another set value, the platform, has to be brought up to generate that variety. For example, the logarithm of 1000 to platform 10 is 3, because 1000 is 10 to the energy 3: 1000 = 10??10??10 = 103. More usually, if x = by, then y is the logarithm of x to platform b, and is published y = logb(x), so log10(1000) = 3.
Logarithms were presented by David Napier in the beginning Seventeenth millennium as a method for quickly simplify calculations. They were quickly implemented by navigators, researchers, technicians, and others to execute calculations more quickly, using fall guidelines and logarithm platforms. Boring multi-digit multiplication actions can be changed by desk look-ups and easier inclusion because of the truth essential in its own right that the logarithm of a item is the sum of the logarithms of the factors
loga mn = loga m + loga n [Product Law]
The above result is capable of extension i.e.
loga (mnp) = loga m + loga n + loga p +
loga m/n = loga m loga n [Quotient Law]
loga mn = n loga m [Power Law]
Example to Solve Logarithms Algebraically
Express log10 a2c/b in terms of log10 a, log10 b, log10 c.
Solution
log10 a2c/b = log10 a2c log10 b [Quotient Law]
= log10 a2 + log10 c log10 (b)1/2 [Product Law]
= 2 log10 a + log10 c 1/2 log10 b [Power Law]
Problems on Solve Logarithms Algebraically
Without using logarithm table, evaluate 3 + log10 (10 2)
