Math / Algebra

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

Studdy Solution

STEP 1

1. The equation involves natural logarithms, denoted by $\ln$ .
2. Simplification of logarithmic expressions will be necessary.
3. The goal is to solve for the variable $x$ .

STEP 2

1. Simplify the equation $\ln x - \ln x + 1 = 2$ .
2. Solve for $x$ .

STEP 3

Simplify the left-hand side of the equation. $\ln x - \ln x + 1 = 0 + 1 = 1$

STEP 4

Set the simplified left-hand side equal to the right-hand side. $1 = 2$

STEP 5

Notice that the equality $1 = 2$ is a contradiction. Therefore, there is no solution to the equation. $\text{No solution}$
Solution: The equation $\ln x - \ln x + 1 = 2$ has no solution because it simplifies to $1 = 2$ , which is a contradiction.

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

Studdy Solution

STEP 1

1. The equation involves natural logarithms, denoted by $\ln$ .
2. Simplification of logarithmic expressions will be necessary.
3. The goal is to solve for the variable $x$ .

STEP 2

1. Simplify the equation $\ln x - \ln x + 1 = 2$ .
2. Solve for $x$ .

STEP 3

Simplify the left-hand side of the equation. $\ln x - \ln x + 1 = 0 + 1 = 1$

STEP 4

Set the simplified left-hand side equal to the right-hand side. $1 = 2$

STEP 5

Notice that the equality $1 = 2$ is a contradiction. Therefore, there is no solution to the equation. $\text{No solution}$
Solution: The equation $\ln x - \ln x + 1 = 2$ has no solution because it simplifies to $1 = 2$ , which is a contradiction.

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Question(3) ln⁡x−ln⁡x+1=2\ln x-\ln x+1=2lnx−lnx+1=2

Studdy Solution

STEP 1

1. The equation involves natural logarithms, denoted by ln⁡\lnln.2. Simplification of logarithmic expressions will be necessary.3. The goal is to solve for the variable xxx.

STEP 2

1. Simplify the equation ln⁡x−ln⁡x+1=2\ln x - \ln x + 1 = 2lnx−lnx+1=2.2. Solve for xxx.

STEP 3

Simplify the left-hand side of the equation. ln⁡x−ln⁡x+1=0+1=1 \ln x - \ln x + 1 = 0 + 1 = 1 lnx−lnx+1=0+1=1

STEP 4

Set the simplified left-hand side equal to the right-hand side. 1=2 1 = 2 1=2

STEP 5

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

1. The equation involves natural logarithms, denoted by $\ln$ .
2. Simplification of logarithmic expressions will be necessary.
3. The goal is to solve for the variable $x$ .

1. Simplify the equation $\ln x - \ln x + 1 = 2$ .
2. Solve for $x$ .

Simplify the left-hand side of the equation. $\ln x - \ln x + 1 = 0 + 1 = 1$

Set the simplified left-hand side equal to the right-hand side. $1 = 2$