Question

Solve the following exponential equation

`3 {}^(2x ) - 9 = 0`
​

Answer 1

3*2x-3*2=0
2x-2=0
2x=2|:2
x=1

Answer 2

x = 1

Explanation:

Given exponential equation:

`3^(2x)-9=0`

Add 9 to both sides of the equation:

`\implies 3^(2x)-9+9=0+9`

`\implies 3^(2x)=9`

`\textsf{Apply exponent rule} \quad a^(bc)=(a^b)^c:`

`\implies \left(3^2\right)^(x)=9`

`\implies9^(x)=9`

`\textsf{Apply exponent rule} \quad a=a^1:`

`\implies9^(x)=9^1`

`\textsf{Apply exponent rule} \quad a^(f(x))=a^(g(x)) \implies f(x)=g(x):`

`\implies x=1`