Question

343^2x-5=49^x/2 solve for x

Answer 1

x = 0

Explanation:

343^(2x) * 49^(-x/2) = 49^(x/2)

(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)

7^(6x) * 7^(-x) = 7^(x)

Now, we can simplify the equation further by combining the like terms on both sides:

7^(6x - x) = 7^(x)

7^(5x) = 7^(x)

We can solve for x by equating the exponents on both sides of the equation:

5x = x

4x = 0

x = 0

Therefore, the solution to the equation is x = 0.

Answer 2

Explanation:

We can start by simplifying the expression using the laws of exponents:

343^(2x) * 49^(-x/2) = 49^(x/2)

We can then simplify further by expressing everything in terms of 7 (since 7 is the common factor of both 343 and 49):

(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)

Applying the laws of exponents again, we get:

7^(6x) * 7^(-x) = 7^x

7^(6x - x) = 7^x

7^(5x) = 7^x

Now we can solve for x by equating the exponents on both sides:

5x = x

4x = 0

x = 0

Therefore, the solution to the equation is x = 0.