# Homework Help: Can I use brackets on the subscript of a log?

1. Jun 18, 2012

### priceofcarrot

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Hi, can I type brackets around the subscript of a log? Can I type brackets around the non subscript as well?

I included what I mean in the picture below, as it's maybe easier to see what I mean. I'm just concerned that the meaning of what I wrote changes when I include the brackets. I don't want it to now mean multiplied where it shouldn't.

Do both forms mean the same thing? Thanks

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2. Jun 18, 2012

### Mentallic

I wouldn't bother with the brackets, just make sure that if you're writing out the subscripts on paper that it's obvious which is which.

By the way, take a look at this proof:

$$\log_ab=x$$
This is equivalent to
$$a^x=b$$
Now, the LHS can become
$$\frac{1}{a^{-x}}=\left(\frac{1}{a}\right)^{-x}$$
Hence we can use the definition of the log again to transform it back into
$$\log_{1/a}b=-x$$

3. Jun 18, 2012

### priceofcarrot

Sorry, but why did you include that? I'm just confused. I appreciate it though.

Anyway, I'd like to use the brackets if possible, just because when I write my calculations in Word, a subscript '1/3' looks kind of weird to me, because it doesn't look like 1 over 3.

Thanks

4. Jun 18, 2012

### LCKurtz

The parentheses won't hurt anything. Go ahead and use them.

5. Jun 18, 2012

### Mentallic

Because if $$\log_ab=x$$ and $$\log_{1/a}b=-x$$ then $$\log_{1/a}b=-\log_ab$$ hence you can change your log expressions from $\log_{1/7}3$ to $-\log_73$

6. Jun 18, 2012

### priceofcarrot

Oh great, thanks to both of you.