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# Pre calc help solve for x?

How do you solve this

Solve for x

1). (2 / 2 ^log5 x ) = 1/16

2). log(x^2 -1)=2+log (x+1)

Find all the roots or zeros for the following polynomial

F(x)= x^4 -2x^3 +5x^2 -8x +4

### 2 Answers

- 7 years ago
I'm trying to make heads-and-tails of what you're asking for in problem 1, but it's just not happening

log(x^2 - 1) = 2 + log(x + 1)

log(x^2 - 1) - log(x + 1) = 2

log((x^2 - 1) / (x + 1)) = 2

(x^2 - 1) / (x + 1) = 10^2

(x^2 - 1) = 100 * (x + 1)

x^2 - 1 = 100x + 100

x^2 - 100x - 1 - 100 = 0

x^2 - 100x - 101 = 0

(x - 101) * (x + 1) = 0

x = -1 , 101

x = -1 isn't valid since log(t) only exists if t > 0

x^4 - 2x^3 + 5x^2 - 8x + 4

x^4 - 2x^3 + x^2 + 4x^2 - 8x + 4

x^2 * (x^2 - 2x + 1) + 4 * (x^2 - 2x + 1)

(x^2 + 4) * (x^2 - 2x + 1)

(x^2 + 4) * (x - 1)^2

(x - 1)^2 = 0

x - 1 = 0

x = 1

x^2 + 4 = 0

x^2 = -4

x = -2i , 2i

x = -2i , 2i , 1