Use the base-change formula to find the logarithm to fourdecimal places. log_5(2.56)

scherezade29pc

scherezade29pc

Answered question

2022-07-28

Use the base-change formula to find the logarithm to fourdecimal places.
log 5 ( 2.56 )

Answer & Explanation

Abraham Norris

Abraham Norris

Beginner2022-07-29Added 16 answers

Use the base-change formula tofind the logarithm to four decimal places.
log 5 ( 2.56 )
The change of base formula is: log b x = log a x log a b
Here b=5 and a=10 (because log x = log 10 x).
log 5 ( 2.56 ) = log 10 ( 2.56 ) log 10 5 = log ( 2.56 ) log 5 0.5841
Darryl English

Darryl English

Beginner2022-07-30Added 2 answers

Use the base-change formula tofind the logarithm to four decimal places.
log 5 ( 2.56 ) = log 5 ( 256 100 ) = log 5 ( 65 25 ) = log 5 ( 64 ) log 5 ( 25 )
= log 5 ( 26 ) log 5 ( 52 ) = 2 log 5 2 2 log 5 5 = 2 log 5 2 2
= 2 ( log 5 2 1 ) = 2 ( log 5 ( 10 / 5 ) 1 ) = 2 ( 2 log 5 10 log 5 5 1 )
= 2 ( 2 log 5 10 2 ) = 2 ( log 10 log 5 2 ) = 2 ( 1 log 5 2 ) 2 ( 1.4307 2 )

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