Find the value of x that solves the equation ln(x-1)+ln 5=2. Answer:

Combine Logarithmic Terms: Combine the logarithmic terms using the property ln(a) + ln(b) = ln(a * b). ln(x - 1) + ln(5) = ln((x - 1) * 5)Set Equal to 2: Set the combined logarithmic expression equal to 2. ln(5(x - 1)) = 2Exponentiate Both Sides: Exponentiate both sides of the equation to remove the natural logarithm, using the property e^(ln(a)) = a. e^(ln(5(x - 1))) = e^2Simplify Left Side: Simplify the left side of the equation, knowing that e and ln are inverse functions. 5(x - 1) = e^2Calculate e^2: Calculate e^2 to get an approximate value. e^2 ≈ 7.389Divide to Isolate: Divide both sides of the equation by 5 to isolate (x - 1). (x - 1) = e^2 / 5 (x - 1) ≈ 7.389 / 5Calculate Division: Calculate the division to simplify the right side of the equation. (x - 1) ≈ 1.478Add 1 to Solve: Add 1 to both sides of the equation to solve for x. x ≈ 1.478 + 1 x ≈ 2.478

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Find the value of
x that solves the equation
ln(x-1)+ln 5=2.
Answer:

Find the value of $x$ that solves the equation $\ln (x-1)+\ln 5=2$ . $\newline$ Answer:

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Algebra 2

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Q. Find the value of

x

that solves the equation

\ln (x-1)+\ln 5=2

\newline

Answer:

Combine Logarithmic Terms: Combine the logarithmic terms using the property $\ln(a) + \ln(b) = \ln(a \cdot b)$ . $\ln(x - 1) + \ln(5) = \ln((x - 1) \cdot 5)$
Set Equal to $2$ : Set the combined logarithmic expression equal to $2$ . $\ln(5(x - 1)) = 2$
Exponentiate Both Sides: Exponentiate both sides of the equation to remove the natural logarithm, using the property $e^{\ln(a)} = a$ . $\newline$ $e^{\ln(5(x - 1))} = e^2$
Simplify Left Side: Simplify the left side of the equation, knowing that $e$ and $\ln$ are inverse functions. $\newline$ $5(x - 1) = e^2$
Calculate $e^2$ : Calculate $e^2$ to get an approximate value. $e^2 \approx 7.389$
Divide to Isolate: Divide both sides of the equation by $5$ to isolate $(x - 1)$ . $\newline$ $(x - 1) = \frac{e^2}{5}$ $\newline$ $(x - 1) \approx \frac{7.389}{5}$
Calculate Division: Calculate the division to simplify the right side of the equation. $x - 1$ ≈ $1.478$
Add $1$ to Solve: Add $1$ to both sides of the equation to solve for $x$ . $x \approx 1.478 + 1$ $x \approx 2.478$