To solve this equation, we need to isolate the variable x.
First, rewrite the equation as:
2^(3x-1) * 7^(3x-1) = 196
Next, rewrite 196 as a product of prime factors:
196 = 2^2 * 7^2
Now, substitute 196 with its prime factorization in the equation:
2^(3x-1) 7^(3x-1) = 2^2 7^2
Since the bases on both sides are the same, we can equate the exponents:
3x - 1 = 23x - 1 = 2
Solve for x:
3x = 2 + 13x = 3x = 1
Therefore, the solution to the equation is x = 1.
To solve this equation, we need to isolate the variable x.
First, rewrite the equation as:
2^(3x-1) * 7^(3x-1) = 196
Next, rewrite 196 as a product of prime factors:
196 = 2^2 * 7^2
Now, substitute 196 with its prime factorization in the equation:
2^(3x-1) 7^(3x-1) = 2^2 7^2
Since the bases on both sides are the same, we can equate the exponents:
3x - 1 = 2
3x - 1 = 2
Solve for x:
3x = 2 + 1
3x = 3
x = 1
Therefore, the solution to the equation is x = 1.