Question

Solve for x. 9^x+15=3^7x

Answer 1

The solution is x = 6

Step-by-step explanation:

Let us revise some rules of the exponents

• If $a^{n}=a^{m}$ , then n = m
• $(a^{n})^{m}=a^{nm}$

∵ $9^{(x+15)}=3^{7x}$

∵ 9 = 3 × 3

∴ 9 = 3²

- Substitute 9 by 3² in the equation above

∴ $(3^{2})^{(x+15)}=3^{7x}$

- Use the second rule above for the left hand side

∵ $(3^{2})^{(x+15)}=3^{2(x+15)}$

∴ $(3^{2})^{(x+15)}=3^{2x+30}$

∴ $3^{2x+30}=3^{7x}$

- 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

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