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Solve for [tex]\( x \)[/tex].

[tex]\[ 5^{5x} = 25 \][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution is [tex]\( x = \square \)[/tex]. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)

B. The solution is not a real number.

Sagot :

GinnyAnswer
To solve the equation [tex]\( 5^{5x} = 25 \)[/tex]:

1. Recognize the relationship between bases and exponents:
- The base on the left-hand side of the equation is 5, and 25 can be expressed as a power of 5.
- Note that [tex]\( 25 = 5^2 \)[/tex].

2. Rewrite the equation using the same base:
[tex]\[ 5^{5x} = 5^2 \][/tex]

3. Equate the exponents (since the bases are the same, the exponents must be equal):
[tex]\[ 5x = 2 \][/tex]

4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{2}{5} \][/tex]

Thus, the solution is:
[tex]\[ \boxed{\frac{2}{5}} \][/tex]

So, the correct answer is:
A. The solution is [tex]\( x = \frac{2}{5} \)[/tex].
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