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]
