Let us discuss about the log proof examples. The logarithm is the power to the base value. It is normally declare the my = p the logarithm of p, the m is the base value y. There are many properties are used in the logarithm. Next we see the proofs of product rule and proofs of quotient rule. In this article we shall discuss about the log proofs examples.
Log Proofs:
First proofs for the product rule Logm ab = logm a + logm b.
Proofs:
The first step is let p = logm a and q = logm b.
The second step is write in exponent form a = a p and b = a q
The third step is multiply the a and b
a • b = a p • a q
= a p+q
The fourth step is take log m of both sides and evaluate
log m ab = log m m p+q
log m ab = (p +q) log m m
log m ab = m + n
log m ab = logm a + logm b
The result is Logm ab = logm a + logm b.
Next proof for the quotient rule, the rule is logm (a/b) = logm a- logm b
Proofs:
The first step is let p = logm a and q = logm b
The second step is write in exponent form
a = m p and b = m q
The third step is divide a by b
a ÷ b = m p ÷ m q = m p –q
The fourth step is take log m of both sides and evaluate
log m (a ÷ b) = log m m p – q
log m (a ÷ b) = (p – q) log m m
log m (a ÷ b) = p – q
log m (a ÷ b) = logm a – logm b
The result is logm (a/b) = logm a- logm b
Log Proofs Examples:
Examples problem for log proofs
Example 1:
Calculate the logarithm value is log54002
Solution
Log 5 400 2 = 2 log5 400
= 2 log5 (20 x 20)
= 2 (log5 20 + log5 20)
= 2 (2 log5 20 )
= 4 log5 20
The answer is 4 log5 20
Example 2:
Calculate the logarithm value is log4 (4/2)
Solution
log4 (4/2) = log44 – log4 2
= log422 - log 42
= 2 log42 – log 42
= log42 (2-1)
= log42
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