Need help with expressing this logarithm Express log_3(a^2 +sqrt(b)) in terms of m and k where m=log3a Given this information I made a=3^m b=3^k

tonan6e

tonan6e

Answered question

2022-09-01

Need help with expressing this logarithm
Express l o g 3 ( a 2 + b ) in terms of m and k where m = l o g 3 a
k = l o g 3 b
Given this information I made a = 3 m
b = 3 k
Therefore = l o g 3 ( ( 3 m ) 2 + ( 3 k ) ) 1 2
= l o g 3 ( 3 2 m + 3 k 2 )
I don't know if I'm done or there is still more things I can simplify. Can anyone help please, thanks

Answer & Explanation

Phoenix Owen

Phoenix Owen

Beginner2022-09-02Added 6 answers

Since there is no expansion for log ( a + b ), hence, you could stop there. If you need to get an approximation(sometimes in computer science), you could use log ( a + b ) = log a + log ( 1 + b / a ), then you have following:
2 m + log 3 ( 1 + 3 k / 2 2 m ) .

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