# Solve equation for X: 125^(3x) = 1/5^(18) (so far, I have (125)^{3x} * 5^{18} = 1)

#### richiesmasher

##### Junior Member
Solve this equation for X

125[SUP]3x[/SUP] =1/5[SUP]18

[/SUP]
So far I have , (125)[SUP]3x * [/SUP]5[SUP]18 [/SUP]= 1

What kind of steps are required here?

Or I was thinking perhaps writing the expression as such

125[SUP]3x[/SUP] = 5[SUP]-18[/SUP]

#### lev888

##### Junior Member
125[SUP]3x[/SUP] = 5[SUP]-18[/SUP]
Looks good. How do we get a simple equation from this?

#### Dr.Peterson

##### Elite Member
125[SUP]3x[/SUP] = 5[SUP]-18[/SUP]
Hint: when you are solving exponential equations, it's a good idea to be familiar with powers of 2, 3, 4, 5 so you can recognize them when you see them. In particular, since one base is 5, it would be very nice if 125 was a power of 5, wouldn't it?

#### richiesmasher

##### Junior Member
Looks good. How do we get a simple equation from this?
Got it:
125[SUP]3x[/SUP] =5[SUP]-18[/SUP]

= (5[SUP]3[/SUP])[SUP]3x[/SUP]= 5[SUP]-18[/SUP]

5[SUP]9x[/SUP]=5[SUP]-18[/SUP]

(because both bases are the same)

9x=-18
x= -2