Find x value from the equation 3^(7-2x)=5^(4x+11)

Take ln of both sides: Given the equation 3^(7-2x) = 5^(4x+11), we will use logarithms to solve for x. Take the natural logarithm (ln) of both sides of the equation to utilize the property that ln(a^b) = b*ln(a). ln(3^(7-2x)) = ln(5^(4x+11))Apply logarithmic property: Apply the logarithmic property to both sides of the equation. (7-2x)*ln(3) = (4x+11)*ln(5)Distribute ln values: Distribute ln(3) and ln(5) on both sides of the equation. 7*ln(3) - 2x*ln(3) = 4x*ln(5) + 11*ln(5)Rearrange terms: Rearrange the terms to isolate x on one side of the equation. -2x*ln(3) - 4x*ln(5) = 11*ln(5) - 7*ln(3)Factor out x: Factor out x from the left side of the equation. x*(-2*ln(3) - 4*ln(5)) = 11*ln(5) - 7*ln(3)Divide to solve for x: Divide both sides by (-2*ln(3) - 4*ln(5)) to solve for x. x = (11*ln(5) - 7*ln(3)) / (-2*ln(3) - 4*ln(5))Calculate numerical value: Calculate the numerical value of x using the values of ln(3) and ln(5). x ≈ (11*ln(5) - 7*ln(3)) / (-2*ln(3) - 4*ln(5))

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Find $x$ value from the equation $\newline$ $3^{7-2x}=5^{4x+11}$

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Algebra 2

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Q. Find

x

value from the equation

\newline

3^{7-2x}=5^{4x+11}

Take ln of both sides: Given the equation $3^{7-2x} = 5^{4x+11}$ , we will use logarithms to solve for $x$ . $\newline$ Take the natural logarithm (ln) of both sides of the equation to utilize the property that $\ln(a^b) = b\cdot\ln(a)$ . $\newline$ $\ln(3^{7-2x}) = \ln(5^{4x+11})$
Apply logarithmic property: Apply the logarithmic property to both sides of the equation. $\newline$ $(7-2x)\ln(3) = (4x+11)\ln(5)$
Distribute ln values: Distribute $\ln(3)$ and $\ln(5)$ on both sides of the equation. $\newline$ $7\cdot\ln(3) - 2x\cdot\ln(3) = 4x\cdot\ln(5) + 11\cdot\ln(5)$
Rearrange terms: Rearrange the terms to isolate $x$ on one side of the equation. $\newline$ $-2x\ln(3) - 4x\ln(5) = 11\ln(5) - 7\ln(3)$
Factor out $x$ : Factor out $x$ from the left side of the equation. $\newline$ $x*(-2*\ln(3) - 4*\ln(5)) = 11*\ln(5) - 7*\ln(3)$
Divide to solve for $x$ : Divide both sides by $(-2\ln(3) - 4\ln(5))$ to solve for $x$ . $x = \frac{11\ln(5) - 7\ln(3)}{-2\ln(3) - 4\ln(5)}$
Calculate numerical value: Calculate the numerical value of $x$ using the values of $\ln(3)$ and $\ln(5)$ . $x \approx (11\cdot\ln(5) - 7\cdot\ln(3)) / (-2\cdot\ln(3) - 4\cdot\ln(5))$