Answer:
[tex] \huge{ \bold{ \boxed{ \sf{x = \frac{1}{3} }}}}[/tex]
☪ First , Let's know about Exponential Equation :
⤿ Let's take an equation : [tex] \sf{ {2}^{x} = 8}[/tex].
In this equation , the variable ' x ' is the exponent of the base 2. Such an equation in which variable appears as an exponent of a base is known as exponential equation. The following axioms are useful while solving the exponential equations :
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☯ Now , Let's Solve :
[tex] \underline{ \sf{Given \: Exponential \: Equation \: : {8}^{x} = 2}}[/tex]
In this equation , the variable 'x' is the exponent of the base 8 .Write [tex] \sf{ {8}^{x} }[/tex] in exponential form with the base of 2
↦ [tex] \sf{ {2}^{3x} = 2}[/tex]
Write the number 2 in exponential form with the base of 2.
↦ [tex] \sf{ {2}^{3x} = {2}^{1}} [/tex]
Since the bases are same , cut 2 on both sides and set the exponents equal.
↦ [tex] \sf{ { \cancel{2}} \: ^{3x} = { \cancel{2} } \: ^{1} }[/tex]
↦ [tex] \sf{3x = 1}[/tex]
Divide both sides by 3
↦ [tex] \sf{ \frac{3x}{3} = \frac{1}{3}} [/tex]
↦ [tex]\boxed{ \bold{ \sf{x = \frac{1}{3} }}}[/tex]
And we're done!
Hope I helped!
Have a wonderful day! ツ
~TheAnimeGirl ♡
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