Solve(Using Logarithms) Another problem I can't quite figure out: 1/2 ln(a+1)+ln5=1 Solve using logarithms. Thank you!

Josiah Owens

Josiah Owens

Answered question

2022-10-20

Solve(Using Logarithms)
Another problem I can't quite figure out:
1 2 ln ( a + 1 ) + ln 5 = 1
Solve using logarithms.
Thank you!

Answer & Explanation

rcampas4i

rcampas4i

Beginner2022-10-21Added 22 answers

You need to use the following identity:
ln a + ln b = ln a b
ln ( a + 1 ) 1 2 + ln 5 = 1
ln 5 ( a + 1 ) 1 2 = 1
5 ( a + 1 ) 1 2 = e 1
25 ( a + 1 ) = e 2
a = e 2 25 1
Deja Bradshaw

Deja Bradshaw

Beginner2022-10-22Added 4 answers

Using m log ( c ) = log ( c m ) where both logarithm remain defined
ln ( a + 1 ) + 2 ln 5 = 2 ln ( a + 1 ) + ln ( 5 2 ) = 2
Again, using log ( x ) + log ( y ) = log ( x y ) where both logarithm remain defined
ln { 25 ( a + 1 ) } = 2
25 ( a + 1 ) = e 2

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