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Solve for
x, rounding to the nearest hundredth.

2^(x)=12
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $2^{x}=12$ $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. Solve for

x

, rounding to the nearest hundredth.

\newline

2^{x}=12

\newline

Answer:

Write Equation: Write down the equation. $\newline$ We are given the equation $2^x = 12$ . We need to solve for $x$ .
Apply Logarithm: Apply the logarithm to both sides of the equation. $\newline$ To solve for $x$ , we can use logarithms. Applying the natural logarithm ( $\ln$ ) to both sides gives us $\ln(2^x) = \ln(12)$ .
Use Power Rule: Use the power rule of logarithms. $\newline$ The power rule of logarithms states that $\ln(a^b) = b\cdot\ln(a)$ . We can apply this rule to simplify the left side of the equation: $x\cdot\ln(2) = \ln(12)$ .
Isolate $x$ : Isolate $x$ . $\newline$ To solve for $x$ , we divide both sides of the equation by $\ln(2)$ : $x = \frac{\ln(12)}{\ln(2)}$ .
Calculate x: Calculate the value of x using a calculator. $\newline$ Using a calculator, we find that $\ln(12) \approx 2.48490665$ and $\ln(2) \approx 0.69314718$ . Now we divide these two values to find x: $x \approx \frac{2.48490665}{0.69314718}$ .
Perform Division: Perform the division to find the value of $x$ . After dividing, we get $x \approx 3.584962501$ . Rounding this to the nearest hundredth gives us $x \approx 3.58$ .

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