log 3^(7-2x)=5^(4x+11)

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Recognize Equation Involves Logarithms: First, we need to recognize that the equation involves logarithms and exponents. We will start by simplifying the logarithmic part of the equation. log 3^(7-2x) = 5^(4x+11) Using the property of logarithms that log a^b = b * log a, we can simplify the left side of the equation: (7 - 2x) * log 3 = 5^(4x+11)Simplify Left Side of Equation: Next, we need to deal with the right side of the equation. Since there is no simple way to convert 5^(4x+11) to a base of 3 or to a logarithmic form that would easily allow us to solve for x, we will need to use a different strategy. We can apply logarithms to both sides of the equation to bring the exponents down. We will use the natural logarithm (ln) for this purpose: ln((7 - 2x) * log 3) = ln(5^(4x+11))Apply Natural Logarithm: We apply the natural logarithm to both sides of the equation to bring down the exponents: ln(3^(7-2x)) = ln(5^(4x+11)) Using the property of logarithms that ln(a^b) = b * ln(a), we can simplify both sides: (7 - 2x) * ln(3) = (4x + 11) * ln(5)Simplify Linear Equation: Now we have a linear equation in terms of x that we can solve. We will distribute ln(3) and ln(5) on both sides: 7 * ln(3) - 2x * ln(3) = 4x * ln(5) + 11 * ln(5)Collect Like Terms: Next, we will collect like terms and move all terms involving x to one side of the equation and constants to the other side: -2x * ln(3) - 4x * ln(5) = 11 * ln(5) - 7 * ln(3)Factor Out x: We can 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: Now we will 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 x Value: Finally, we can calculate the 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))

$\log 3^{(7-2x)}=5^{(4x+11)}$

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log⁡3(7−2x)=5(4x+11)\log 3^{(7-2x)}=5^{(4x+11)}log3(7−2x)=5(4x+11)

$\log 3^{(7-2x)}=5^{(4x+11)}$