Question

What is the solution of 9 (x-8) = 3 (4x-12)

() = Exponents The things in perenthacys are exponents

Answer 1

• 9(x-8)=3(4x-12)
• 9x-72=12x-37
• 9x-12x=-72+37
• -3x=-35
• x=-35/-3
• x=35/3

Solving as exponents

`\\ \rm\Rrightarrow 9^((x-8))=3^((4x-12))`

`\\ \rm\Rrightarrow 3^(2(x-8))=3^(2(x-6))`

`\\ \rm\Rrightarrow 2(x-8)=2(x-6)`

`\\ \rm\Rrightarrow 2x-16=4x-12`

`\\ \rm\Rrightarrow -2x=4`

`\\ \rm\Rrightarrow x=-2`

Answer 2

`x=-2`

Explanation:

Given equation:

`9^(x-8)=3^(4x-12)`

Rewrite 9 as 3²:

`\implies (3^2)^(x-8)=3^(4x-12)`

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

`\implies 3^(2(x-8))=3^(4x-12)`

`\implies 3^(2x-16)=3^(4x-12)`

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

`\implies 2x-16=4x-12`

Subtract 2x from both sides:

`\implies 2x-16-2x=4x-12-2x`

`\implies -16=2x-12`

Add 12 to both sides:

`\implies -16+12=2x-12+12`

`\implies -4=2x`

Divide both sides by 2:

`\implies (-4)/(2)=(2x)/(2)`

`\implies x=-2`