To solve the exponential equation [tex]\( 625 = 5^{(7x - 3)} \)[/tex], we need to express [tex]\( 625 \)[/tex] as a power of [tex]\( 5 \)[/tex].
Let's start by recognizing that:
[tex]\[ 625 = 5^4 \][/tex]
This allows us to rewrite the equation as:
[tex]\[ 5^4 = 5^{(7x - 3)} \][/tex]
Since the bases are the same on both sides of the equation, we can set the exponents equal to each other:
[tex]\[ 4 = 7x - 3 \][/tex]
Now, we solve for [tex]\( x \)[/tex]:
1. Add 3 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 4 + 3 = 7x \][/tex]
[tex]\[ 7 = 7x \][/tex]
2. Divide both sides by 7 to solve for [tex]\( x \)[/tex]:
[tex]\[ \frac{7}{7} = x \][/tex]
[tex]\[ x = 1 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{x = 1} \][/tex]
So the correct answer is [tex]\( B. \)[/tex] [tex]\( x = 1 \)[/tex].
