Question

What is the value of x if g^x-1-2= 25?

Answer 1

Answer:

Third option: $x=\frac{5}{2}$

Step-by-step explanation:

The correct exercise is attached.

The equation given is:

$9^{x-1}-2=25$

 The steps to find the value of "x" are shown below:

1. Add 2 to both sides of the equation:

$9^{x-1}-2+2=25+2\\\\9^{x-1}=27$

2. Descompose 9 and 27 into their prime factors:

$9=3*3=3^2\\27=3*3*3=3^3$

3. Substitute them into the equation:

$3^{2(x-1)}=3^3$

4. Knowing that If $a^n=b^m$, then $n=m$, we get:

$2(x-1)=3$

5. Apply Distributive property:

$2x-2=3$

6. Add 2 to both sides:

$2x-2+2=3+2\\\\2x=5$

7. Divide both sides of the equation by 2:

$\frac{2x}{2}=\frac{5}{2}\\\\x=\frac{5}{2}$

Answer 2

Answer:

x = $\frac{5}{2}$

Step-by-step explanation:

this is correct answer on ed-genuity, hope this helps! :)