if (343^{x}=49^{4 - x}), what is the value of (x)?\n(\frac{5}{8})\n(\frac{8}{5})\n2\n8

Explanation:

Step1: Rewrite bases as powers of 7

Since (343 = 7^3) and (49=7^2), the equation (343^{x}=49^{4 - x}) can be rewritten as ((7^{3})^{x}=(7^{2})^{4 - x}).

Step2: Apply power - of - a - power rule

According to the power - of - a - power rule ((a^{m})^{n}=a^{mn}), we get (7^{3x}=7^{2(4 - x)}).

Step3: Set exponents equal

If (a^{m}=a^{n}), then (m = n). So, (3x=2(4 - x)).

Step4: Expand and solve for x

Expand the right - hand side: (3x = 8-2x). Add (2x) to both sides: (3x + 2x=8), which simplifies to (5x = 8). Then (x=\frac{8}{5}).

Answer:

B. (\frac{8}{5})