# Homework Help: What is the inverse of this logarithm equation?

1. Jan 2, 2013

### supernova1203

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

What is the inverse of this logarithm equation?

y=-log5(-x)

i tried it and i got y=-5(-x)

hm.. you know how people say that if you want to find the inverse graph of something just switch the x and y coordinates from the table of values? Well i also tried that approach and apparently the inverse is y=log5x

atleast thats how it looks on table of values and on the graph....i dunno why i went with the y=-5(-x)

I dont know if i got it right or not, someone kind enough to take a look and see if i got it right or not? or maybe just give me the solution outright so i know if i did it correctly or not? :P

Last edited: Jan 2, 2013
2. Jan 2, 2013

### symbolipoint

Your result is correct. If you start from your original equation, multiply both sides by negative 1, you can easily switch x and y, and carry couple simple steps to find y as a function of x.

3. Jan 2, 2013

### supernova1203

hm... so y=log5x is correct?

4. Jan 2, 2013

### symbolipoint

No! Your first result was correct. y=-5^(-x)

5. Jan 2, 2013

ahh ok ty

6. Jan 2, 2013

### symbolipoint

Original equation: $y=-log_{5}(-x)$

$-y=log_{5}(-x)$
Now express exponential form :
$5^{-y}=-x$

Now, switch x and y to create inverse:
$5^{-x}=-y$,

and then simply, $y=-5^{-x}$

7. Jan 2, 2013

### Mentallic

To check if you're right, when you get to the equation $x=-5^{-y}$, just plug that value of x into your original equation $y=-\log_5(-x)$ and see if you get an equality.