Answer:
x = [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
[tex](7^{x})^{4}=\frac{7^{2}\times 7^{3}}{7^{3x}}[/tex]
[tex](7^{x})^{4}=\frac{7^{(2+3)}}{7^{3x}}[/tex] [Since [tex]a^{b}\times a^{c}=a^{b+c}[/tex] ]
[tex]7^{4x}=\frac{7^{5}}{7^{3x}}[/tex] [since [tex](a^{b})^{c}=a^{bc}[/tex] ]
[tex]7^{4x}={7^{5}\times{7^{-3x}}[/tex] [ [tex]\frac{1}{a}=a^{-1}[/tex] ]
[tex]7^{4x}=7^{(5-3x)}[/tex]
4x = 5 - 3x
[tex]4x+3x=5[/tex] ⇒ 7x = 5
x = [tex]\frac{5}{7}[/tex]
