Exponential Equations solve 27^x=1/√3

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SUMMARY

The equation 27^x = 1/√3 can be solved by expressing both sides as powers of 3. This leads to the transformation 3^{3x} = 3^{-\frac{1}{2}}. By equating the exponents, we find that 3x = -1/2, resulting in the solution x = -1/6. This method effectively utilizes properties of exponents to simplify the problem.

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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
 
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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?
 
To follow up, we may write:

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

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

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

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