log x = log(x + 3) - log(x - 1)
Answers
First note that log(x) is defined only for x > 0; log(x + 3) for x > -3; and log(x - 1) for x > 1. So if we find any solutions x ≤ 1, these will be extraneous.
Condense the right side:
log(x) = log((x + 3) / (x - 1))
Let b be the base of the logarithm. Then writing both sides as powers of this b simplifies the equation to
b^log(x) = b^log((x + 3) / (x - 1))
x = (x + 3) / (x - 1)
Solve for x :
x (x - 1) = x + 3
x ² - x = x + 3
x ² - 2x - 3 = 0
(x - 3) (x + 1) = 0
x - 3 = 0 or x + 1 = 0
x = 3 or x = -1
We throw out x = -1 because it's less than 1, so the only (real) solution is x = 3.
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Related Questions
If every 1 in 20 plants will not bear fruit. If 200 plants are planted, how many will produce fruit?
Answers
Answer:
Step-by-step explanation:
If 1 /20 will not bear fruit then
19/20. Will bear fruit
use ratio method
19/20 = x/200
find x by finding an equivalent fraction
x = 190
190 plants will produce fruit
A parallelogram is a rectangle if and only
if its diagonals are congruent.
Answers
Answer:
A parallelogram is a rectangle if and only if its diagonals are congruent. A rectangle is a parallelogram with four right angles. A rhombus is a parallelogram with four congruent sides. If a parallelogram has two consecutive sides congruent, it is a rhombus.
Step-by-step explanation: