Find the exact value of each expression log642Solutionlog642

Find the exact value of each expression.

log64(2)

Solution

log₆₄(2)

=log_2⁸ (2)

=(1/8)log₂(2)............since log_a^c b^d =(d/c)log_ab

=(1/8)*1..................sionce log_aa =1

=1/8

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log₂(64)

=log₂(2⁸)

=(8/1)log₂(2)............since log_a^c b^d =(d/c)log_ab

=(8)*1..................sionce log_aa =1

=8