Respuesta :

Answer:

x = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^m^{n}[/tex] = [tex]a^{mn}[/tex]

Note that 8 = 2³ and 2 = [tex]2^{1}[/tex], then

[tex](2^3)^{x}[/tex] = [tex]2^{1}[/tex], that is

[tex]2^{3x}[/tex] = [tex]2^{1}[/tex]

Since the bases on both sides are equal, equate the exponents

3x = 1 ( divide both sides by 3 )

x = [tex]\frac{1}{3}[/tex]

The value of [tex]x[/tex] is [tex]\dfrac{1}{3}[/tex].

Properties of exponents:

  • [tex](a^m)^n=a^{mn}[/tex]
  • If [tex]x^a=x^b[/tex], , then [tex]a=b[/tex].

The given equation is:

[tex]8^x=2[/tex]

It can be rewritten as:

[tex](2^3)^x=2^1[/tex]

[tex]2^{3x}=2^1[/tex]          [tex][\because (a^m)^n=a^{mn}][/tex]

On comparing the exponents, we get

[tex]3x=1[/tex]

Divide both sides by 3.

[tex]\dfrac{3x}{3}=\dfrac{1}{3}[/tex]

[tex]x=\dfrac{1}{3}[/tex]

Therefore, the required value is .

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