Find the value of x that solves the equation ln(x+2)-(1)/(3)ln 8=ln 2. Answer: x=

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Find the value of  x that solves the equation  ln(x+2)-(1)/(3)ln 8=ln 2. Answer:  x=

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Simplify using properties: To solve the equation ln(x+2)-(1/3)ln 8=ln 2, we first need to simplify the equation by using the properties of logarithms.Rewrite using power rule: Using the power rule of logarithms, which states that ln(a^b) = b*ln(a), we can rewrite (1/3)ln 8 as ln(8^(1/3)).Combine logarithms: Since 8^(1/3) is the cube root of 8, which is 2, we can further simplify the equation to ln(x+2) - ln(2) = ln(2).Equation simplification: Now, we can use the property of logarithms that ln(a) - ln(b) = ln(a/b) to combine the left side of the equation into a single logarithm: ln((x+2)/2) = ln(2).Equating arguments: Since the logarithmic function is one-to-one, if ln(a) = ln(b), then a = b. Therefore, we can equate the arguments of the logarithms: (x+2)/2 = 2.Multiply to solve: To solve for x, we multiply both sides of the equation by 2 to get x+2 = 4.Subtract to find: Finally, we subtract 2 from both sides to find the value of x: x = 4 - 2.Final solution: So, the value of x that solves the equation is x = 2.

Find the value of $x$ that solves the equation $\ln (x+2)-\frac{1}{3} \ln 8=\ln 2$ . $\newline$ Answer: $x=$

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Find the value of $x$ that solves the equation $\ln (x+2)-\frac{1}{3} \ln 8=\ln 2$ . $\newline$ Answer: $x=$