Multiplying Simple Logarithms

Algebra Level 1

( log 2 16 ) × ( log 3 27 ) × ( log 4 64 ) = ? \large (\log _{ 2 }{ 16 }) \times (\log _{ 3 }{ 27 }) \times (\log _{ 4 }{ 64 }) = \ ?

40 30 36 24

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1 solution

Yosua Sibuea
Dec 8, 2015

Thank you for your great answer and also great factorization !

Mark Jacobsen - 5 years, 6 months ago

Great job Yosua Sibea but I will also give you a alternative solution,

log 2 16 = log 2 2 4 = 4 log 3 27 = log 3 3 3 = 3 log 4 64 = log 4 4 3 = 3 \log _{ 2 }{ 16 } =\log _{ 2 }{ { 2 }^{ 4 } } =4\\ \log _{ 3 }{ 27 } =\log _{ 3 }{ { 3 }^{ 3 } } =3\\ \log _{ 4 }{ 64 } =\log _{ 4 }{ { 4 }^{ 3 } } =3

Therefore , multiply the product of the logarithms , 4 × 3 × 3 = 36 4\times 3\times 3=36\\

Therefore, the answer is 36 \boxed{36}

Hint: This also the alternative solution from his solution and always remember when the logarithm and the number of the base is the same the answer is always the exponent of the logarithm and a hint of mine.

Mark Jacobsen - 5 years, 6 months ago

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What is logarithm?

Kimberly Schott - 5 years, 5 months ago

Thank you for the simple solution.helped me understand better.

Sowmiya Vasudevan - 5 years, 5 months ago

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