To solve this equation, we can rewrite it using the properties of exponents:
5^(2x-1) = 0.4 2^(2x-1)5^(2x-1) = 4/10 2^(2x-1)5^(2x-1) = 2/5 * 2^(2x-1)5^(2x-1) = 2^(2x-1) / 5^(1)
Now, we can rewrite the equation to have the same base:
(5/10)^(2x-1) = 2^(2x-1) / 5
Now, we can rewrite 5/10 as 1/2:
(1/2)^(2x-1) = 2^(2x-1) / 5
Now, we can rewrite 1/2 as 2^-1:
2^(-1 * (2x-1)) = 2^(2x-1) / 5
Now that the bases are the same, we can equate the exponents:
-2x + 1 = 2x - 1
Now, let's solve for x:
-2x + 1 = 2x - 11 = 4x - 12 = 4xx = 2/4x = 1/2
Therefore, the solution to the equation 5^(2x-1) = 0.4 * 2^(2x-1) is x = 1/2.
To solve this equation, we can rewrite it using the properties of exponents:
5^(2x-1) = 0.4 2^(2x-1)
5^(2x-1) = 4/10 2^(2x-1)
5^(2x-1) = 2/5 * 2^(2x-1)
5^(2x-1) = 2^(2x-1) / 5^(1)
Now, we can rewrite the equation to have the same base:
(5/10)^(2x-1) = 2^(2x-1) / 5
Now, we can rewrite 5/10 as 1/2:
(1/2)^(2x-1) = 2^(2x-1) / 5
Now, we can rewrite 1/2 as 2^-1:
2^(-1 * (2x-1)) = 2^(2x-1) / 5
Now that the bases are the same, we can equate the exponents:
-2x + 1 = 2x - 1
Now, let's solve for x:
-2x + 1 = 2x - 1
1 = 4x - 1
2 = 4x
x = 2/4
x = 1/2
Therefore, the solution to the equation 5^(2x-1) = 0.4 * 2^(2x-1) is x = 1/2.