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

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

Bytelearn · Accepted Answer

Take Logarithm: Take the natural logarithm of both sides of the equation to utilize the property of logarithms that allows us to bring down the exponents. ln(3^(7-2x)) = ln(5^(4x+11))Apply Property: Apply the logarithmic property ln(a^b) = b*ln(a) to both sides. (7-2x)*ln(3) = (4x+11)*ln(5)Distribute Logarithms: Distribute the natural logarithms on both sides. 7*ln(3) - 2x*ln(3) = 4x*ln(5) + 11*ln(5)Rearrange Equation: Rearrange the equation to group like terms and isolate the variable x on one side. -2x*ln(3) - 4x*ln(5) = 11*ln(5) - 7*ln(3)Factor Out X: Factor out the x on the left side of the equation. x*(-2*ln(3) - 4*ln(5)) = 11*ln(5) - 7*ln(3)Divide by Coefficient: Divide both sides by the coefficient of x to solve for x. x = (11*ln(5) - 7*ln(3)) / (-2*ln(3) - 4*ln(5))Calculate Value: Calculate the value of x using the values of natural logarithms. x ≈ (11*ln(5) - 7*ln(3)) / (-2*ln(3) - 4*ln(5)) x ≈ (11*1.60944 - 7*1.09861) / (-2*1.09861 - 4*1.60944) x ≈ (17.70384 - 7.68927) / (-2.19722 - 6.43776) x ≈ 10.01457 / -8.63498 x ≈ -1.1598

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

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Find `x` value from the equation \newline3(7−2x)=5(4x+11)3^{(7-2x)}=5^{(4x+11)}3(7−2x)=5(4x+11)

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