x is [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Let us revise some rules of exponents
- [tex](a^{n})(a^{n})=a^{m+n}[/tex]
- [tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
- [tex](a^{m})^{n}=a^{mn}[/tex]
- [tex]a^{m}=a^{n}[/tex] , then m = n
∵ [tex]27^{x-1}=9^{3x-7}[/tex]
- Factorize 27 and 9
∵ 27 = 3 × 3 × 3
∴ 27 = 3³
∵ 9 = 3 × 3
∴ 9 = 3²
Substitute them in the equation
∴ [tex](3^{3})^{x-1}=(3^{2})^{3x-7}[/tex]
- Use the third rule to simplify each side
∴ [tex](3)^{3x-3}=(3)^{6x-14}[/tex]
- Use the fourth rule
∵ The bases of the two sides are equal
∴ Their exponents are equal
∴ 3x - 3 = 6x - 14
- Subtract 6x from both sides
∴ -3x - 3 = -14
- Add 3 to both sides
∴ -3x = -11
Divide both sides by -3
∴ x = [tex]\frac{11}{3}[/tex]
x is [tex]\frac{11}{3}[/tex]
Learn more:
You can learn more about equations in brainly.com/question/4934417
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