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what is the value of x in the equation 3^(2x-1)=27?

Sagot :

Answer:

x=2

Explanation:

Given the equation:

[tex]3^{2x-1}=27[/tex]

To solve for x, begin by writing 27 as a power of 3.

[tex]3^{2x-1}=3^3[/tex]

Next, since both sides of the equation have the same base, 3, it follows from the law of indices that:

[tex]\begin{gathered} a^x=a^y\implies x=y \\ \text{Therefore:} \\ 3^{2x-1}=3^3\implies2x-1=3 \end{gathered}[/tex]

We then solve the resulting equation for x.

[tex]\begin{gathered} 2x-1=3 \\ \text{Add 1 to both sides} \\ 2x-1+1=3+1 \\ 2x=4 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{4}{2} \\ x=2 \end{gathered}[/tex]

The value of x in the equation is 2.

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