Find the value of x that solves the equation ln(x-2)-ln 2=0. Answer:

Combine Logarithmic Expressions: Combine the logarithmic expressions using the properties of logarithms. Since ln(a) - ln(b) = ln(a/b), we can combine the two logarithms on the left side of the equation. ln((x-2)/2) = 0Exponentiate Both Sides: Exponentiate both sides of the equation to remove the natural logarithm. e^(ln((x-2)/2)) = e^0 Since e^ln(a) = a, we have (x-2)/2 = 1Solve for x: Solve for x. Multiply both sides of the equation by 2 to isolate (x-2). (x-2) = 2 * 1 (x-2) = 2Add 2 to Solve: Add 2 to both sides of the equation to solve for x. x = 2 + 2 x = 4

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Find the value of
x that solves the equation
ln(x-2)-ln 2=0.
Answer:

Find the value of $x$ that solves the equation $\ln (x-2)-\ln 2=0$ . $\newline$ Answer:

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Grade 7

Write an equivalent ratio

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Q. Find the value of

x

that solves the equation

\ln (x-2)-\ln 2=0

\newline

Answer:

Combine Logarithmic Expressions: Combine the logarithmic expressions using the properties of logarithms. $\newline$ Since $\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ , we can combine the two logarithms on the left side of the equation. $\newline$ $\ln\left(\frac{x-2}{2}\right) = 0$
Exponentiate Both Sides: Exponentiate both sides of the equation to remove the natural logarithm. $\newline$ $e^{\ln(\frac{x-2}{2})} = e^0$ $\newline$ Since $e^{\ln(a)} = a$ , we have $\frac{x-2}{2} = 1$
Solve for x: Solve for x. $\newline$ Multiply both sides of the equation by $2$ to isolate $(x-2)$ . $\newline$ $(x-2) = 2 \times 1$ $\newline$ $(x-2) = 2$
Add $2$ to Solve: Add $2$ to both sides of the equation to solve for $x$ . $x = 2 + 2$ $x = 4$