# Homework Help: Logs question

1. Dec 11, 2004

### seiferseph

if log2 = x and log3 = y, solve for log(base5)36 in terms of x and y.

can someone help me get started with this one? thanks.

Last edited: Dec 11, 2004
2. Dec 11, 2004

### primarygun

Try to use the translation of base formula.
Or let log(base 5)10=z
Try to think of how to convert log5 in terms of x.
Notice that some special value you can get, such as log2=x , log3=y, log1=0, log 10=1,etc.
Then you can express it in term of x.

3. Dec 11, 2004

### HallsofIvy

What is the base in the original log, 10?

Assuming you mean log10(2)= x and log10(3)= y,

log5(10)= 1/log10(5).

5= 10/2 so log10(5)= log10(10/2)= log10(10)- log10(2)= 1- x.

log10(3) doesn't enter into it.

4. Dec 11, 2004

### seiferseph

i'll post a little bit of what i've done, the teacher said its simple, and in the last questions we've converted the bases for x and y to the one for the final, not the other way around. heres what i've done, not sure if its right.

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Last edited: Dec 11, 2004
5. Dec 11, 2004

### seiferseph

sorry, its supposed to be log(base5)36 to solve for

6. Dec 11, 2004

### Zurtex

36 = 3*3*2*2

Now apply the fact that: log(ab) = log(a) + log(b)

7. Dec 11, 2004

### seiferseph

so in the end i get

log(base5)36 = 2x + 2y / log(base10)5
can it be simplified further?

8. Dec 11, 2004

### primarygun

Yes.
log 5=1-x

9. Dec 11, 2004

### Zurtex

You sure you have read the edits?

10. Dec 14, 2004

### primarygun

What's edited?

11. Dec 14, 2004

### Zurtex

The original question.