MHB Exponential Equations solve 27^x=1/√3

[Fright535]

I'm taking an online class and I was doing some very simple exponential equations when this was thrown at me, and I have no clue how to solve it.

27^x=1/√3

 

[MarkFL]

Hello, and welcome to MHB! (Wave)

We are given to solve:

$$27^x=\frac{1}{\sqrt{3}}$$

Can you write both sides of the equation as a power of 3?

 

[MarkFL]

To follow up, we may write:

$$3^{3x}=3^{-\frac{1}{2}}$$

Since we have like bases, we can simply equate the exponents:

$$3x=-\frac{1}{2}\implies x=-\frac{1}{6}$$