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

Answer:

$x=-2$

Step-by-step 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:

$\implies \dfrac{-4}{2}=\dfrac{2x}{2}$

$\implies x=-2$