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