Using Logarithms − 2 n − 1 ln ⁡ 2 = − 100 ln ⁡...

DIAMMIBENVERMk1

DIAMMIBENVERMk1

Answered

2022-07-08

Using Logarithms
2 n 1 ln 2 = 100 ln 10 100 ln 10 = 230 230 ln ( 2 ) = 333 2 n 1 > 333 ( n 1 ) ln ( 2 ) > ln ( 333 )
Here is where I am stuck.
I am not sure if this part is correct: n 1 = 8. Then solving we would get 9

Answer & Explanation

Camron Herrera

Camron Herrera

Expert

2022-07-09Added 16 answers

Log is an increasing function. So you can take log in both side of an inequality and that is fine. But you can't take log of negative values like -2 The mistake is at
2 n 1 = 333.
You missed negative sign at 333. Then if you correct the next steps it's fine. Also when you multiply both sides of an inequality by negative the sign changes.
2 n 1 l n 2 < 100 l n 10
2 n 1 < 100 l n 10 l n 2
2 n 1 > 100 l n 10 l n 2
n 1 l n ( 2 ) > l n ( 100 l n 10 l n 2 ) .
And this gives n > l n ( 100 l n 10 l n 2 ) l n 2 + 1

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