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$8^{\frac{x}{3}} = 2$

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Find the missing exponent or base

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Q.

8^{\frac{x}{3}} = 2

Rewrite $8$ as $2^3$ : We are given the equation $8^{(x/3)} = 2$ . We know that $8$ can be expressed as $2^3$ . Let's rewrite $8$ in terms of $2$ .
Apply power rule: Replace $8$ with $2^3$ in the equation. $\newline$ $(2^3)^{(x/3)} = 2$ $\newline$ Now, apply the power of a power rule, which states that $(a^b)^c = a^{(b*c)}$ .
Simplify left side: Simplify the left side of the equation using the power of a power rule. $\newline$ $2^{3*(x/3)} = 2$ $\newline$ $2^{x} = 2$
Set exponents equal: Since the bases are the same on both sides of the equation, we can set the exponents equal to each other. $x = 1$

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