What is the effect of error on a calculation, and what are the components of error that are often considered?

March 22, 2026Mathematics

ScanSolve AI Answer

March 22, 2026

Answer

x=2

Step 1: Apply the logarithm property $\ln a + \ln b = \ln(ab)$ for $a>0$ , $b>0$ .

\ln[(x+1)(x-1)] = \ln 3

Step 2: Since $\ln$ is one-to-one, equate the arguments.

(x+1)(x-1) = 3

Step 3: Expand the left side.

x^2 - 1 = 3

Step 4: Solve for $x^2$ .

x^2 = 4

x = \pm 2

Step 5: Determine the domain where both arguments are positive: $x+1 > 0$ and $x-1 > 0$ .

x > 1

Step 6: Check candidate solutions in the domain.

For $x=2 > 1$ : valid.
Verify: $\ln(3) + \ln(1) = \ln 3 + 0 = \ln 3$ .

For $x=-2 < 1$ : $\ln(-1)$ undefined in reals. Invalid.

Final answer

x=2

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Quick Answer

[(x+1)(x-1)] = 3 Step 2: Since is one-to-one, equate the arguments.
(x+1)(x-1) = 3 Step 3: Expand the left side.
x^2 - 1 = 3 Step 4: Solve for x^2.
x^2 = 4 x = ± 2 Step 5: Determine the domain where both arguments are positive: x+1 > 0 and x-1 > 0.

Asked on March 22, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 22, 2026

Step 1: Apply the logarithm property a + b = (ab) for a>0, b>0. [(x+1)(x-1)] = 3 Step 2: Since is one-to-one, equate the arguments. (x+1)(x-1) = 3 Step 3: Expand the left side. x^2 - 1 = 3 Step 4: Solve for x^2. x^2 = 4 x = ± 2 Step 5: Determine the domain where both arguments are positive: x+1 > 0 and x-1 > 0. x > 1 Step 6: Check candidate solutions in the domain. For x=2 > 1: valid. Verify: (3) + (1) = 3 + 0 = 3. For x=-2 < 1: (-1) undefined in reals. Invalid. Final answer x=2