Question #252442

Solve for the values of x for each of the following exponential equations and inequalities.


1. 82-2


2. () <=


3. 5* = 25-2


4. 3x+2 à ¢ ‰ ¥ 27


5. 43x 8-1


1
Expert's answer
2021-10-18T15:08:56-0400

1.

82x=28^{2-x}=2

82x=81/38^{2-x}=8^{1/3}

2x=132-x=\dfrac{1}{3}

x=53x=\dfrac{5}{3}

2.

(12)x<18(\dfrac{1}{2})^{x}<\dfrac{1}{8}

(12)x<(12)3(\dfrac{1}{2})^{x}<(\dfrac{1}{2})^{3}

x>3x>3

3.

5x=25x25^x=25^{x-2}

25x/2=25x225^{x/2}=25^{x-2}

x2=x2\dfrac{x}{2}=x-2

x2=2\dfrac{x}{2}=2

x=4x=4


4.

3x+2273^{x+2}\geq27

3x+2333^{x+2}\geq3^3

x+23x+2\geq3

x1x\geq1

5.

43x=8x14^{3x}=8^{x-1}

26x=23x32^{6x}=2^{3x-3}

6x=3x36x=3x-3

3x=33x=-3

x=1x=-1







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