Question

Hi, how's everyone doing? I need help with these exponential equations, please. Thanks! :)​

Answer 1

Answer:

Step-by-step explanation:

1). $2^{x^{2} +2x}=\frac{1}{2}$

  $2^{x^{2} +2x}=2^{-1}$

  Comparing exponents on both the sides.

  x² + 2x = -1

  x² + 2x + 1 = 0

  (x + 1)² = 0

  x = -1

2). $2^{x-3}=8^{x+1}$

  $2^{x-3}=(2^{3})^{x+1}$

  $2^{x-3}=(2)^{3(x+1)}$

  By comparing exponents,

  x - 3 = 3(x + 1)

  x - 3 = 3x + 3

  3x - x = 3 + 3

  2x = 6

  x = 3

3). $\sqrt{a^{5-k}}=a^{3-k}$

   $a^{\frac{5-k}{2}}=a^{3-k}$

   By comparing exponents,

   $\frac{5-k}{2}=3-k$

   5 - k = 2(3 - k)

   5 - k = 6 - 2k

   2k - k = 6 - 5

    k = 1

4). $3^{x+3}=27^{(2x+6)}$

    $3^{x+3}=(3^3)^{2x+6}$

    $3^{x+3}=(3)^{3(2x+6)}$

    By comparing exponents,

    x + 3 = 3(2x + 6)

    x + 3 = 6x + 18

    6x - x = 3 - 18

    5x = - 15

    x = -3

5). $5^{x-2}=1$

    $5^{(x-2)}=5^{0}$

    x - 2 = 0

    x = 2