Answer :

1. The solution of the expression for x is 5/2.

2. The solution of the expression for x is 2.

Given that;

The expressions are,

1. [tex]25^x = 3125[/tex]

2. [tex]49^x= 2401[/tex]

Now simplify the expression for x;

1. [tex]25^x = 3125[/tex]

Since, 5 x 5 x 5 x 5 x 5 = 3125

5⁵ = 3125

Hence the expression is written as,

[tex](5^2)^x = (5^5)[/tex]

[tex]5^{2x} = 5^5[/tex]

After comparison,

[tex]2x = 5[/tex]

[tex]x = \dfrac{5}{2}[/tex]

2. [tex]49^x= 2401[/tex]

Since 7 x 7 x 7 x 7 = 2401

7⁴ = 2401

Hence the expression is written as,

[tex](7^2)^x = 7^4[/tex]

[tex]7^{2x} = 7^4[/tex]

After comparison,

[tex]2x = 4[/tex]

[tex]x = 2[/tex]

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The complete question is,

Simplify the expressions for the value of x.

1. [tex]25^x = 3125[/tex]

2. [tex]49^x= 2401[/tex]

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