Find the value of x that solves the equation ln(x-2)-2ln 4=ln 1. Answer: x=

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Find the value of  x that solves the equation  ln(x-2)-2ln 4=ln 1. Answer:  x=

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Simplify the equation: First, we need to simplify the equation using properties of logarithms. The equation is ln(x-2) - 2ln(4) = ln(1). We know that ln(1) is equal to 0 because the natural logarithm of 1 is always 0. So, the equation simplifies to ln(x-2) - 2ln(4) = 0.Apply logarithmic properties: Next, we can use the property of logarithms that states ln(a^b) = b*ln(a) to simplify the term 2ln(4). This gives us ln(x-2) - ln(4^2) = 0. Since 4^2 is 16, this simplifies further to ln(x-2) - ln(16) = 0.Combine logarithmic terms: Now, we can use another property of logarithms that allows us to combine the two logarithmic terms into one by division inside the logarithm: ln(a) - ln(b) = ln(a/b). This gives us ln((x-2)/16) = 0.Remove natural logarithm: To solve for x, we need to get rid of the natural logarithm. We can exponentiate both sides of the equation with base e to remove the ln, which gives us e^(ln((x-2)/16)) = e^0. Since e^0 is 1, and e^(ln(y)) is y for any y, we have (x-2)/16 = 1.Solve for x: Finally, we solve for x by multiplying both sides of the equation by 16. This gives us x-2 = 16. Adding 2 to both sides gives us x = 16 + 2, which simplifies to x = 18.

Find the value of $x$ that solves the equation $\ln (x-2)-2 \ln 4=\ln 1$ . $\newline$ Answer: $x=$

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Find the value of x x x that solves the equation ln⁡(x−2)−2ln⁡4=ln⁡1 \ln (x-2)-2 \ln 4=\ln 1 ln(x−2)−2ln4=ln1.\newlineAnswer: x= x= x=

Find the value of $x$ that solves the equation $\ln (x-2)-2 \ln 4=\ln 1$ . $\newline$ Answer: $x=$