Recognize Equation Type: Recognize that the equation is an exponential equation. We need to find the value of x such that 3^x equals 17. Since 17 is not a power of 3, we will likely need to use logarithms to solve for x.Apply Logarithm: Apply the logarithm to both sides of the equation. Taking the natural logarithm (ln) of both sides gives us ln(17) = ln(3^x).Use Power Rule: Use the power rule of logarithms. The power rule of logarithms states that ln(a^b) = b * ln(a). Applying this rule, we get ln(17) = x * ln(3).Solve for x: Solve for x. To isolate x, we divide both sides of the equation by ln(3). This gives us x = ln(17) / ln(3).Calculate x Value: Calculate the value of x. Using a calculator, we find that x ≈ ln(17) / ln(3) ≈ 2.579. However, the question prompt asks for the answer as an integer or a fraction in simplest form. Since x is not an integer and cannot be expressed as a simple fraction, we leave it in this logarithmic form.

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$2$ ) $17=3^{x}$

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Algebra 2

Solve exponential equations by rewriting the base

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17=3^{x}

Recognize Equation Type: Recognize that the equation is an exponential equation. $\newline$ We need to find the value of $x$ such that $3^x = 17$ . Since $17$ is not a power of $3$ , we will likely need to use logarithms to solve for $x$ .
Apply Logarithm: Apply the logarithm to both sides of the equation. $\newline$ Taking the natural logarithm (ln) of both sides gives us $\ln(17) = \ln(3^x)$ .
Use Power Rule: Use the power rule of logarithms. The power rule of logarithms states that $\ln(a^b) = b \cdot \ln(a)$ . Applying this rule, we get $\ln(17) = x \cdot \ln(3)$ .
Solve for x: Solve for x. $\newline$ To isolate $x$ , we divide both sides of the equation by $\ln(3)$ . This gives us $x = \frac{\ln(17)}{\ln(3)}$ .
Calculate x Value: Calculate the value of $x$ . Using a calculator, we find that $x \approx \frac{\ln(17)}{\ln(3)} \approx 2.579$ . However, the question prompt asks for the answer as an integer or a fraction in simplest form. Since $x$ is not an integer and cannot be expressed as a simple fraction, we leave it in this logarithmic form.