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Solve for
x, rounding to the nearest hundredth.

2^(x)=7
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $2^{x}=7$ $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

2^{x}=7

\newline

Answer:

Apply Logarithm: Apply the logarithm to both sides of the equation $2^x = 7$ . $\newline$ $\log(2^x) = \log(7)$
Use Power Property: Use the power property of logarithms to bring the exponent $x$ in front of the log. $\newline$ $x \cdot \log(2) = \log(7)$
Isolate $x$ : Isolate $x$ by dividing both sides of the equation by $\log(2)$ . $\newline$ $x = \frac{\log(7)}{\log(2)}$
Calculate $x$ : Calculate the value of $x$ using a calculator. $x = \frac{\log(7)}{\log(2)}$ $x = 2.807354922057604107\ldots$
Round to Nearest Hundredth: Round the calculated value of $x$ to the nearest hundredth. $x \approx 2.81$

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