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Solve the exponential equation for [tex]$x$[/tex].

[tex]\[ 625=5^{(7x-3)} \][/tex]

A. [tex]$x=-2$[/tex]
B. [tex]$x=1$[/tex]
C. [tex][tex]$x=-1$[/tex][/tex]
D. [tex]$x=2$[/tex]

Sagot :

GinnyAnsweridn
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].
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