log 3 to the base 3 + log 9 to the base 3 = log 125 to the base 5
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Answer: 3
Step-by-step explanation:
log3 + log 9 (both in base 3) = log 125 base 5
Applying multiplication rule of logarithm:
log n + log p = lognp
⇒ log(3×9) in base 3 = log125 in base 5
⇒log3³ (in base 3) = log5³ (in base 5)
Applying power rule of logarithm:
⇒3log 3 (in base 3) = 3log 5 (in base 5)
⇒ 3 = 3
⇒ LHS = RHS
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