Short Answer x = - 6
Remark
You gave the second best answer.

The trick here is not to divide both sides by 2. Solve the problem this way.

log_5(x + 1)^2 = 2 Take the antilog of both sides
(x + 1)^2 = 5^2 Expand the equation
x^2 + 2x + 1 = 25 Subtract 25 from both sides.
x^2 + 2x - 24 = 0 Factor
(x + 6)(x - 4) = 0 Find the zeros.

x + 6 = 0
x = - 6 <<<<<<<< Answer. This is the extraneous root.
The reason this is an extraneous root is that x<=0 do not have a logarithem

x - 4 = 0
x = 4 This is a legitimate result to the original equation.

7 0

2 years ago

Read 2 more answers

What is the error due to using linear interpolation to estimate the value of sinxsin⁡x at x = \pi/3? your answer should have at

Serhud [2]

<h3>Answer:</h3>

using y = x, the error is about 0.1812
using y = (x -π/4 +1)/√2, the error is about 0.02620

<h3>Step-by-step explanation:</h3>

The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.

If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...

... x -sin(x) @ x=π/3

... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812

You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.

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If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...

... (x+1-π/4)/√2 -sin(x) @ x=π/3

... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620

6 0

2 years ago