Question

equação exponencial
​

Answer 1

Resposta:

Explicação passo a passo:

$a)$

$10^{x+1} =10^{2}$

$x+1=2$

$x=2-1$

$x=1$

$b)$

$(7^{-1}) ^{x-\frac{7}{2} }=7^{\frac{1}{2} }$

$7^{-x+\frac{7}{2} }=7^{\frac{1}{2} }$

$-x+\frac{7}{2}=\frac{1}{2}$

$\frac{7}{2}-\frac{1}{2}=x$

$x=\frac{6}{2}$

$x=3$

$c)$

$4^{2x+50} =4^{0}$

$2x+50=0$

$x=-50/2$

$x=-25$

$d)$

$11^{x}=11^{3}$

$x=3$

$Obs.:1331=11^{3}$

Answer 2

Explicação passo-a-passo:

$a)10 {}^{x + 1} = 100 \\ 10 {}^{x + 1} = 10 {}^{2}$

$x + 1 = 2 \\ x = 2 - 1 \\ x = 1$

$b)( \frac{1}{7} ) {}^{x - \frac{7}{2} } = \sqrt{7}$

$(7 {}^{ - 1} ) {}^{x - \frac{7}{2} } = 7 {}^{ \frac{1}{2} }$

$7 {}^{ - x + \frac{ \frac{}{7} }{2} } = 7 {}^{ \frac{1}{2} }$

$- x + \frac{7}{2} = \frac{1}{2}$

M.m.c=2

-2x+7=1

-2x=1-7

-2x=-6 ×(-1)

2x=6

x=6/2

x=3

$c)4 {}^{2x + 50} = 1 \\ \\ 4 {}^{2x + 50} = 4 {}^{0}$

$2x + 50 = 0 \\ 2x = - 50 \\ x = - \frac{50}{2}$

$x = - 25$

$d)11 {}^{x} = 1.331$

$x = 11 {}^{3}$

$x = 3$