Solve for x, rounding to the nearest hundredth. 2*3^(2x)=1 Answer:

Understand and Isolate Exponential Term: Understand the equation and isolate the exponential term. We have the equation 2*3^(2x) = 1. To solve for x, we first need to isolate the term with the exponent. We do this by dividing both sides of the equation by 2. 3^(2x) = 1/2Take Logarithm to Solve: Take the logarithm of both sides to solve for the exponent. To solve for the exponent 2x, we can take the natural logarithm (ln) of both sides of the equation. ln(3^(2x)) = ln(1/2)Apply Power Rule of Logarithms: Apply the power rule of logarithms. The power rule of logarithms states that ln(a^b) = b*ln(a). We apply this rule to the left side of the equation. 2x * ln(3) = ln(1/2)Solve for x: Solve for x. Now we can solve for x by dividing both sides of the equation by 2*ln(3). x = ln(1/2) / (2*ln(3))Calculate x Value: Calculate the value of x using a calculator. Using a calculator, we find: x ≈ ln(0.5) / (2*ln(3)) x ≈ -0.69314718056 / (2*1.09861228867) x ≈ -0.69314718056 / 2.19722457734 x ≈ -0.31546487678 Rounded to the nearest hundredth, x ≈ -0.32

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Solve for
x, rounding to the nearest hundredth.

2*3^(2x)=1
Answer:

Solve for $x$ , rounding to the nearest hundredth. $\newline$ $2 \cdot 3^{2 x}=1$ $\newline$ Answer:

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Q. Solve for

x

, rounding to the nearest hundredth.

\newline

2 \cdot 3^{2 x}=1

\newline

Answer:

Understand and Isolate Exponential Term: Understand the equation and isolate the exponential term. $\newline$ We have the equation $2\cdot3^{2x} = 1$ . To solve for $x$ , we first need to isolate the term with the exponent. We do this by dividing both sides of the equation by $2$ . $\newline$ $3^{2x} = \frac{1}{2}$
Take Logarithm to Solve: Take the logarithm of both sides to solve for the exponent. $\newline$ To solve for the exponent $2x$ , we can take the natural logarithm (ln) of both sides of the equation. $\newline$ $\ln(3^{2x}) = \ln(\frac{1}{2})$
Apply Power Rule of Logarithms: Apply the power rule of logarithms. The power rule of logarithms states that $\ln(a^b) = b \cdot \ln(a)$ . We apply this rule to the left side of the equation. $2x \cdot \ln(3) = \ln(\frac{1}{2})$
Solve for x: Solve for x. $\newline$ Now we can solve for x by dividing both sides of the equation by $2\ln(3)$ . $\newline$ $x = \frac{\ln(\frac{1}{2})}{2\ln(3)}$
Calculate x Value: Calculate the value of x using a calculator. $\newline$ Using a calculator, we find: $\newline$ $x \approx \frac{\ln(0.5)}{(2\cdot\ln(3))}$ $\newline$ $x \approx \frac{-0.69314718056}{(2\cdot1.09861228867)}$ $\newline$ $x \approx \frac{-0.69314718056}{2.19722457734}$ $\newline$ $x \approx -0.31546487678$ $\newline$ Rounded to the nearest hundredth, $x \approx -0.32$