Question

prove he first law of logarithms ​

Answer 1

Answer:

The laws apply to logarithms of any base but the same base must be used throughout a calculation. This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB.

Step-by-step explanation:

Proof of Change of base Rule Law:

and loga b = z ⇒ az = b. Therefore x = yz or, loga M = Iogb M × loga b [putting the values of x, y, and z]. i.e., the logarithm of a positive numberprove he first law of logarithms Proof of the Product Property of Logarithm

Simplify by applying the product rule of exponent. That is, copy the common base then add the exponents. Step 4: Take the logarithms of both sides of the equation. a with respect to a positive base b (≠ 1) is equal to the reciprocal of logarithm of b with respect to the base a.The laws apply to logarithms of any base but the same base must be used throughout a calculation. This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB.