Answer:
Third option: [tex]x=\frac{5}{2}[/tex]
Step-by-step explanation:
The correct exercise is attached.
The equation given is:
[tex]9^{x-1}-2=25[/tex]
The steps to find the value of "x" are shown below:
1. Add 2 to both sides of the equation:
[tex]9^{x-1}-2+2=25+2\\\\9^{x-1}=27[/tex]
2. Descompose 9 and 27 into their prime factors:
[tex]9=3*3=3^2\\27=3*3*3=3^3[/tex]
3. Substitute them into the equation:
[tex]3^{2(x-1)}=3^3[/tex]
4. Knowing that If [tex]a^n=b^m[/tex], then [tex]n=m[/tex], we get:
[tex]2(x-1)=3[/tex]
5. Apply Distributive property:
[tex]2x-2=3[/tex]
6. Add 2 to both sides:
[tex]2x-2+2=3+2\\\\2x=5[/tex]
7. Divide both sides of the equation by 2:
[tex]\frac{2x}{2}=\frac{5}{2}\\\\x=\frac{5}{2}[/tex]
