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Nastasia [14]
3 years ago
5

Solve the following equations. √3 ⋅ 3^3x = 9

Mathematics
1 answer:
GREYUIT [131]3 years ago
5 0

Answer:

The solution is x = 0.5

Step-by-step explanation:

We need to write everything as a power of 3.

We know that:

\sqrt{a} = a^{0.5}

So

\sqrt{3} = 3^{0.5}

And

9 = 3^{2}

This following property is also important:

\frac{a^{b}}{a^{c}} = a^{b-c}

To solve, the first step is putting everything with the variable x on one side and everything without the variable x on the other side

\sqrt{3}.3^{3x} = 9

3^{0.5}.3^{3x} = 3^{2}

3^{3x} = \frac{3^{2}}{3^{0.5}}

3^{3x} = 3^{2-0.5}

3^{3x} = 3^{1.5}

This means that:

3x = 1.5

x = \frac{1.5}{3}

x = 0.5

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