To solve these equations, we will first simplify the expressions:
(7^x)^3 = 343This can be simplified as 7^(x*3) = 3437^(3x) = 7^3Therefore, 3x = 3x = 1
(25^x) = √5Since 25 can be expressed as 5^2, the equation can be rewritten as:(5^2)^x = √55^(2x) = 5^(1/2)Therefore, 2x = 1/2x = 1/4
So the solutions to the equations are x = 1 and x = 1/4.
To solve these equations, we will first simplify the expressions:
(7^x)^3 = 343
This can be simplified as 7^(x*3) = 343
7^(3x) = 7^3
Therefore, 3x = 3
x = 1
(25^x) = √5
Since 25 can be expressed as 5^2, the equation can be rewritten as:
(5^2)^x = √5
5^(2x) = 5^(1/2)
Therefore, 2x = 1/2
x = 1/4
So the solutions to the equations are x = 1 and x = 1/4.