x = [tex]\frac{5}{7}[/tex]
using the ' laws of exponents '
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{( m + n )}[/tex]
• [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m - n)}[/tex]
• ([tex]a^{m}[/tex])^n = [tex]a^{mn}[/tex]
[tex]7^{2}[/tex] × [tex]7^{3}[/tex] = [tex]7^{5}[/tex] ÷ [tex]7^{3x}[/tex] = [tex]7^{5 - 3x}[/tex]
[tex]7^{4x}[/tex] = [tex]7^{5 - 3x}[/tex]
equating the exponents since bases on both sides are 7
4x = 5 - 3x
7x = 5 ⇒ x =[tex]\frac{5}{7}[/tex]
