The solution is x = 6
Step-by-step explanation:
Let us revise some rules of the exponents
- If [tex]a^{n}=a^{m}[/tex] , then n = m
- [tex](a^{n})^{m}=a^{nm}[/tex]
∵ [tex]9^{(x+15)}=3^{7x}[/tex]
∵ 9 = 3 × 3
∴ 9 = 3²
- Substitute 9 by 3² in the equation above
∴ [tex](3^{2})^{(x+15)}=3^{7x}[/tex]
- Use the second rule above for the left hand side
∵ [tex](3^{2})^{(x+15)}=3^{2(x+15)}[/tex]
∴ [tex](3^{2})^{(x+15)}=3^{2x+30}[/tex]
∴ [tex]3^{2x+30}=3^{7x}[/tex]
- By using the first rule above
∴ 2x + 30 = 7x
- Subtract 2x from both sides
∴ 30 = 5x
- Divide both sides by 5
∴ 6 = x
The solution is x = 6
Learn more:
You can learn more about solving equations in brainly.com/question/7153188
#LearnwithBrainly
