Answer :
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.