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  1. MHB Apprentice

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    #1
    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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  3. Pessimist Singularitarian
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    #2
    Hello, and welcome to MHB!

    We are given to solve:

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

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

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    #3
    To follow up, we may write:

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

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

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

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