Logarithm Evaluating i'm new to this site and I need help on this logarithm question. I don't know how to approach this question to simplify it.log_2(81)/(2−log_2(18)) Apparently the answer is −(4ln(3))/ln(9/2)

Kevin Charles

Kevin Charles

Answered question

2022-10-18

Logarithm Evaluating
i'm new to this site and I need help on this logarithm question. I don't know how to approach this question to simplify it.
log 2 ( 81 ) 2 log 2 ( 18 )
Apparently the answer is 4 ln ( 3 ) ln ( 9 2 )

Answer & Explanation

Teagan Zamora

Teagan Zamora

Beginner2022-10-19Added 18 answers

Use log a ( b m ) = m log a b when both logarithm remain defined unlike
log a 1 = log a ( 1 ) 2 = 2 log a ( 1 )
and log a ( b c ) = log a b + log a c when both logarithm remain defined unlike log a 6 = log a ( 3 ) ( 2 ) = log a ( 3 ) + log a ( 2 ) for real a > 0
Observe that 81 = 3 4
Cristofer Watson

Cristofer Watson

Beginner2022-10-20Added 1 answers

You can start going directly from base 2 to base e and write
log 2 ( 81 ) 2 log 2 ( 18 ) = log ( 81 ) log ( 2 ) ( 2 log ( 18 ) log ( 2 ) ) = log ( 81 ) 2 log ( 2 ) log ( 18 ) = log ( 81 ) log ( 4 ) log ( 18 )
and continue simplifying since
log ( 81 ) = log ( 3 4 ) = 4 log ( 3 )
and
log ( 4 ) log ( 18 ) = log ( 18 4 ) = log ( 9 2 )

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