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

Combine Logarithmic Terms: We are given the equation ln(x-3) = 1 + ln 2. To solve for x, we need to isolate x on one side of the equation. First, we can use the property of logarithms that allows us to combine the terms on the right side of the equation.Rewrite Using Logarithmic Property: We know that ln a + ln b = ln(ab). So we can rewrite the right side of the equation as ln(2e), where e is the base of the natural logarithm and is approximately equal to 2.71828. ln(x-3) = ln(2e)Equate Arguments of Logarithms: Since the natural logarithm function ln is a one-to-one function, if ln(a) = ln(b), then a = b. Therefore, we can equate the arguments of the logarithms from both sides of the equation. x - 3 = 2eSolve for x: Now, we solve for x by adding 3 to both sides of the equation. x = 2e + 3Substitute and Calculate: We substitute the approximate value of e into the equation to find the numerical value of x. x ≈ 2(2.71828) + 3 x ≈ 5.43656 + 3 x ≈ 8.43656

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

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Q. Find the value of

x

that solves the equation

\ln (x-3)=1+\ln 2

\newline

Answer:

Combine Logarithmic Terms: We are given the equation $\ln(x-3) = 1 + \ln 2$ . To solve for $x$ , we need to isolate $x$ on one side of the equation. First, we can use the property of logarithms that allows us to combine the terms on the right side of the equation.
Rewrite Using Logarithmic Property: We know that $\ln a + \ln b = \ln(ab)$ . So we can rewrite the right side of the equation as $\ln(2e)$ , where $e$ is the base of the natural logarithm and is approximately equal to $2.71828$ . $\newline$ $\ln(x-3) = \ln(2e)$
Equate Arguments of Logarithms: Since the natural logarithm function $\ln$ is a one-to-one function, if $\ln(a) = \ln(b)$ , then $a = b$ . Therefore, we can equate the arguments of the logarithms from both sides of the equation. $x - 3 = 2e$
Solve for x: Now, we solve for x by adding $3$ to both sides of the equation. $\newline$ $x = 2e + 3$
Substitute and Calculate: We substitute the approximate value of $e$ into the equation to find the numerical value of $x$ . $\newline$ $x \approx 2(2.71828) + 3$ $\newline$ $x \approx 5.43656 + 3$ $\newline$ $x \approx $8$.$43656$