SOLUTION: Express log_4(7) in terms of natural logarithms. Don't find a numerical answer. --log_4(7) AKA log base 4 of 7 ---- I am not sure how to answer this, what are the steps t

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Express log_4(7) in terms of natural logarithms. Don't find a numerical answer. --log_4(7) AKA log base 4 of 7 ---- I am not sure how to answer this, what are the steps t      Log On


   

Question 1093236: Express log_4(7) in terms of natural logarithms. Don't find a numerical answer.

--log_4(7) AKA log base 4 of 7
---- I am not sure how to answer this, what are the steps to solve this type of problem?
Found 2 solutions by Alan3354, KMST:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Express log_4(7) in terms of natural logarithms.
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log%284%2C7%29+=+ln%284%29%2Fln%287%29
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It's the base change formula.
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Also, log%284%2C7%29+=+log%284%29%2Flog%287%29
Also, log%284%2C7%29+=+log%28b%2C4%29%2Flog%28b%2C7%29 where b is any legal base.

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If x=log%284%2C7%29 , then 4%5Ex=7 .
taking logarithms base e on both sides of that equation,
we find the equivalent equation
ln%284%5Ex%29=ln%287%29 .
using the properties of logarithms, we get
x%2Aln%284%29=ln%287%29 , and solving for x we get
x=highlight%28ln%287%29%2Fln%284%29%29 .