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Solve for
x, rounding to the nearest hundredth.

2^(2x)=5
Answer:

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

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Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

2^{2 x}=5

\newline

Answer:

Apply Logarithm: Apply the logarithm to both sides of the equation $2^{2x} = 5$ . $\newline$ $\log(2^{2x}) = \log(5)$
Use Power Property: Use the power property of logarithms to bring down the exponent. $2x \cdot \log(2) = \log(5)$
Isolate x: Isolate x by dividing both sides of the equation by $2 \cdot \log(2)$ . $\newline$ $x = \frac{\log(5)}{2 \cdot \log(2)}$
Calculate x: Calculate the value of x using a calculator. $\newline$ $x = \frac{\log(5)}{2 \cdot \log(2)}$ $\newline$ $x = \frac{0.69897}{2 \cdot 0.30103}$ $\newline$ $x = \frac{0.69897}{0.60206}$ $\newline$ $x \approx 1.16096404744$
Round to Nearest: Round the value of $x$ to the nearest hundredth. $x \approx 1.16$

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