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### High School Mathematics3.18 Logarithm of a Product

 Log x ab = log x a + log x b. Proof: log x ab = p, therefore ab = xp--------I Let log x a = q, a = xq---------------II log x b = r, b = xr----------III From I and II, ab = xq.xr = xq+r from I, ab = xp------IV from I, II, III and IV, we get xp = xq+r Therefore, p = q + r Therefore, log x ab = log x a + log x b The logarithm of the product of two numbers is equal to the sum of the logarithms of those to numbers. Example: log 2 3*5 = log 2 3 + log 2 5. Directions: Solve the following problems. Also write at least five examples of your own.
 Q 1: log 10 5 + log 10 5 = _________.log 10 5log 10 10log 10 25None of these Q 2: log 5 3 + log 5 2 = _________.log 5 5log 5 6log 5 3log 5 2 Q 3: log 3 5 + log 3 7 = _________.log 3 7log 3 12log 3 5log 3 35 Q 4: log 8 9 + log 8 7 = _________.log 8 63log 8 7log 8 9log 8 16 Q 5: log 6 2 + log 6 8 = _________.log 6 16log 6 2log 6 10log 6 8 Q 6: log 4 3 + log 4 8 = _________.log 4 3log 4 24log 4 8log 4 11 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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