7Âˇ Prove that first law of logarithms ? (Learn all laws)

1.	7Âˇ Prove that first law of logarithms ? (Learn all laws)
Answer» The first law is product rule: logₐ xy = logₐ x + logₐ y Step 1: Let m = logaₐ x and n = logₐ y Step 2: Write in exponent form x = a^m and y = a^n Step 3: Multiply x and y x • y = a^m • a^n = a^(m+n) Step 4: Take log a of both sides and evaluate logₐ xy = logₐ am+nlogₐ xy = (m + n) logₐ alogₐ xy = m + nlogₐ xy = logₐ x + logₐ y Tan q

Answer»

The first law is product rule: logₐ xy = logₐ x + logₐ y

Step 1:

Let m = logaₐ x and n = logₐ y

Step 2: Write in exponent form

x = a^m and y = a^n

Step 3: Multiply x and y

x • y = a^m • a^n = a^(m+n)

Step 4: Take log a of both sides and evaluate

logₐ xy = logₐ am+nlogₐ xy = (m + n) logₐ alogₐ xy = m + nlogₐ xy = logₐ x + logₐ y

Tan q

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