SOLUTION: Write in terms of the NATURAL LOG. (ln) 1. log (base 4)x 2. log (base 10) (x+1) 3. log (base 5) x^4

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write in terms of the NATURAL LOG. (ln) 1. log (base 4)x 2. log (base 10) (x+1) 3. log (base 5) x^4      Log On


   

Question 284540: Write in terms of the NATURAL LOG. (ln)
1. log (base 4)x
2. log (base 10) (x+1)
3. log (base 5) x^4
Found 2 solutions by solver91311, jsmallt9:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Use the base conversion formula:



So, for your first one:




John

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for converting a logarithm of one base into an expression of logarithms of another base is: log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29 (Note where the argument and the base of the original logarithm (on the left) end up on the right side.)

We will use this to convert your logarithms into natural logarithms (aka ln). I'll do the last one first because it is harder than the other two.
log%285%2C+%28x%5E4%29%29
Using the conversion formula on this we get:
ln%28x%5E4%29%2Fln%285%29
This may be an acceptable answer. But we could use a property of logarithms, log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29, to move the exponent of the argument in the numerator out in front:
4ln%28x%29%2Fln%285%29

The other two problems are just one step. I'll leave them for you to finish. Just use the conversion formula like I did above.