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

0 Step-by-step explanation:x-5x+3x²-2x+7= 7 x-1÷7=0did i do good let me know in the commits...

Hi, how s everyone doing? I need help with these

Ответ:

sandeebassett3

17.03.2021

Mathematics

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

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

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