Question

8^x=2 8 to the power of x = 2. Find the value of x.

Answer 1

Answer:

$\huge{ \bold{ \boxed{ \sf{x = \frac{1}{3} }}}}$

☪ First , Let's know about Exponential Equation :

⤿ Let's take an equation : $\sf{ {2}^{x} = 8}$.

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 :

• If $\sf{ {a}^{x} = {a}^{b} }$ , then $\sf{x = b}$
• If $\sf{ {a}^{x} = 1}$ , then $\sf{ {a}^{x} = {a}^{0} }$ and x = 0

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☯ Now , Let's Solve :

$\underline{ \sf{Given \: Exponential \: Equation \: : {8}^{x} = 2}}$

In this equation , the variable 'x' is the exponent of the base 8 .Write $\sf{ {8}^{x} }$ in exponential form with the base of 2

↦ $\sf{ {2}^{3x} = 2}$

Write the number 2 in exponential form with the base of 2.

↦ $\sf{ {2}^{3x} = {2}^{1}}$

Since the bases are same , cut 2 on both sides and set the exponents equal.

↦ $\sf{ { \cancel{2}} \: ^{3x} = { \cancel{2} } \: ^{1} }$

↦ $\sf{3x = 1}$

Divide both sides by 3

↦ $\sf{ \frac{3x}{3} = \frac{1}{3}}$

↦ $\boxed{ \bold{ \sf{x = \frac{1}{3} }}}$

And we're done!

Hope I helped!

Have a wonderful day! ツ

~TheAnimeGirl ♡

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