Use the properties of logarithms to write the logarithm in terms of log_3 5 and log_3 7 log_3 (45)/(49)

Joglxym

Joglxym

Answered question

2022-11-04

Use the properties of logarithms to write the logarithm in terms of log 3 5 and log 3 7
log 3 45 49

Answer & Explanation

mentest91k99

mentest91k99

Beginner2022-11-05Added 17 answers

We have to use the properties of logarithms to write the logarithm in the terms of log 3 5 and log 3 7.
Using the properties of logarithmic functions,
log m n = log m log n log a b = b log a log ( m n ) = log m + log n
and it is also known that log e e = 1
Now 45 can be written as 3.3.5 and 49 can be written as 7.7
log 3 43 45 = log 3 45 log 3 49 = log 3 ( 3.3.5 ) log 3 ( 7.7 ) = log 3 ( 3 2 .5 ) log 3 ( 7 2 ) = log 3 ( 3 2 ) + log 3 ( 5 ) log 3 ( 7 2 ) = 2 log 3 3 + log 3 ( 5 ) 2 log 3 ( 7 ) = 2 + log 3 ( 5 ) 2 log 3 ( 7 )
Hence expression is 2 + log 3 ( 5 ) 2 log 3 ( 7 )

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