Exponent Problem on CAT

[nefcooper]

Hi there was an exponent problem on one of the CAT's and I got stuck at this point in the answer explanation:

Step 1: 3^(2x+18) = 1
Step 2: 3^ (2x+18) = 3^0
Step 3: 2x+18=0
Step 4: 2x=-18
Step 5: x=-9


Could you explain how they went from Step 2 to Step 3 please?

[noamfishman]

Hi Nefcooper,

I think in step 2 they set both sides of the equation to have the same base (3). For the equation to be equal, both sides' exponents must equal each other.

Step 3 is an equation with both exponents, set equal to each other.

I hope this helps.

[nefcooper]

Thanks. Yea I understand that part of it, but what did they do to make the base of 3 disappear in step 3? I don't understand what rule was used to get rid of the base.

Thanks!

[RonPurewal]

Thanks. Yea I understand that part of it, but what did they do to make the base of 3 disappear in step 3? I don't understand what rule was used to get rid of the base.

Thanks!

If 3^this = 3^that, then this = that.

The best way to conceptualize this is just to think about how exponents behave. If x is bigger than y, then 3^x is going to be bigger than 3^y, always. So, if two powers of 3 are the same, they have to be the same power.

You're not going to get this to be an algebraic step, unless you want to think about logarithms. (You don't want to.)

[nefcooper]

aha! Got it. Thanks!!

[RonPurewal]

You're welcome.