Solve the following exponential equation: `3^(6 - 3x) = 1/27`

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to express the term to the right side as 3 raised to a power such that: `27 = 3^3` .

Writing the equation using the powers of 3 yields:

`3^(6-3x)=1/(3^3)`

`` You need to remember that `1/(3^3) = 3^(-3), ` hence:

`3^(6-3x)=3^(-3)`

Notice that the bases both sides are alike, hence you may equate exponents such that:

`6 - 3x = -3`

Isolating -3x to the left side yields:

`-3x = -3 - 6 =gt -3x = -9 =gt x = 3`

Hence, the solution to the exponential equation is x = 3.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation `3^(6 - 3x) = 1/27` has to be solved for x.

`3^(6 - 3x) = 1/27`

=> `3^(6 - 3x) = 1/3^3`

=> `3^(6 - 3x) = 3^(-3)`

As the base is the same on both the sides the exponent can be equated, which gives 6 - 3x = -3

=> 3x = 9

=> x = 3

The solution of the equation is x = 3

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