Question

A solução da equação exponencial 81^2x-10 = 3^x . 9, é:. A) 6 B)7 C)5 D)4 E)8​

Answer 1

$3^{\left(4\left(2x-10\right)\right)}=3^x\cdot \:3^2\\\\Aplicar \ as \ propriedade \ dos \ expoentes\\\\ 4\left(2x-10\right)=x+2\\\\Resolver \ 4\left(2x-10\right)=x+2\\\\a=4,\:b=2x,\:c=10\\\\4\cdot \:2x-4\cdot \:10\\\\8x-40\\\\8x-40=x+2\\\\\mathrm{Adicionar\:}40\mathrm{\:a\:ambos\:os\:lados}\\\\8x-40+40=x+2+40\\\\\mathrm{Simplificar}\\\\8x=x+42\\\\\mathrm{Subtrair\:}x\mathrm{\:de\:ambos\:os\:lados}\\\\8x-x=x+42-x\\\\\mathrm{Simplificar}\\\\7x=42$

$\mathrm{Dividir\:ambos\:os\:lados\:por\:}7\\\\\frac{7x}{7}=\frac{42}{7}\\\\42:7=6\\\\\mathrm{Simplificar}\\\\x=6$

Answer 2

Resposta:

A) 6

Explicação passo a passo:

A solução da equação exponencial 81^2x-10 = 3^x . 9

3^[4(2x-10)] = 3^x . 3^2

3^[4.(2x-10)] = 3^(x+2)

4.(2x-10) = x + 2

8x - 40 = x + 2

8x - x = 2+40

7x = 42

X = 42/7

X = 6

R.:

A) 6