Answer:
\(x={\frac{8}{5}\)
Step-by-step explanation:
The given equation is:
\(343^x=49^{4-x}\)
Create equivalent expressions in the equation that all have equal bases, thus
\(7^{3(x)}=7^{2(4-x)}\)
Since the bases are the same, then two expressions are only equal if the exponents are also equal, thus
\(3(x)=2(4-x)\)
\(3x=8-2x\)
\(5x=8\)
\(x={\frac{8}{5}\)
which is the required value of x.
