Question

mod

best users

prove it no definition Prove product law of logrithem please ​

Answer 1

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Answer 2

We have to prove :-

$log_{a}(mn) = log_{a}(m) + log_{a}(n)$

Proff :-

Let

$log_{a}(m) \: \: be \: x \: \: (log \: form)$

${a}^{x} = m \: ( \: exponential \: form \: ) \: - (1)$

Let

$log_{a}(n) \: be \: y \: ( \: log \: form \: )$

${a}^{y} = n \: ( \: exponential \: form) - (2)$

Multiplying 1 and 2

${a}^{x} \times {a}^{y} = mn$

➵ ${a}^{x + y} = mn \: (exponential \: form \: )$

➵ $log_{a}(mn) = log_{a}(m) + log_{a}(n) \: ( \: log \: form \: )$

Now give value of of x and y

$log_{a}(mn) = log_{a}(m) + log_{a}(n)$

Hence proffed the product law

Know more :-

There are many laws of logarithm some of them are

• Product law :-

Logrithm of the product of numbers is equal to sum of logrithm of numbers

• Quotient law or division law :-

The logarithm of quotient of two numbers is equal to difference of logarithm of numbers

• Power law :-

The logarithm of a number is raised by the power "n" and is equal to "n" times the logarithm of that number