Solve for x, rounding to the nearest hundredth. 4*2^((x)/(5))=1 Answer:

Isolate exponential term: First, we need to isolate the exponential term on one side of the equation. Since we are given 4*2^(x/5) = 1, we can divide both sides by 4 to get 2^(x/5) = 1/4.Recognize fraction as negative exponent: Next, we recognize that 1/4 is 2^(-2) because 2^(-2) = 1/(2^2) = 1/4. So we can rewrite the equation as 2^(x/5) = 2^(-2).Set exponents equal: Since the bases are the same and the equation is an equality, we can set the exponents equal to each other. This gives us x/5 = -2.Multiply to isolate x: To solve for x, we multiply both sides of the equation by 5 to isolate x. This gives us x = -2 * 5.Final solution: Multiplying -2 by 5 gives us x = -10.

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Solve for
x, rounding to the nearest hundredth.

4*2^((x)/(5))=1
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $4 \cdot 2^{\frac{x}{5}}=1$ $\newline$ Answer:

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Q. Solve for

x

, rounding to the nearest hundredth.

\newline

4 \cdot 2^{\frac{x}{5}}=1

\newline

Answer:

Isolate exponential term: First, we need to isolate the exponential term on one side of the equation. Since we are given $4\cdot2^{x/5} = 1$ , we can divide both sides by $4$ to get $2^{x/5} = \frac{1}{4}$ .
Recognize fraction as negative exponent: Next, we recognize that $\frac{1}{4}$ is $2^{-2}$ because $2^{-2} = \frac{1}{2^2} = \frac{1}{4}$ . So we can rewrite the equation as $2^{\frac{x}{5}} = 2^{-2}$ .
Set exponents equal: Since the bases are the same and the equation is an equality, we can set the exponents equal to each other. This gives us $\frac{x}{5} = -2$ .
Multiply to isolate $x$ : To solve for $x$ , we multiply both sides of the equation by $5$ to isolate $x$ . This gives us $x = -2 \times 5$ .
Final solution: Multiplying $-2$ by $5$ gives us $x = -10$ .