Question

Lg(0,5+x)+lgx=lg0,5________________

Answer 1

Используется формула суммы логарифмов с одинаковым основанием.
lg(0.5x + x^2) = lg(0.5)
ОДЗ: x>0
0.5x + x^2 = 0.5
x^2 + 0.5x - 0.5 = 0
D = 2.25
x1 = (-0.5 + 1.5)/2 = 1/2
x2 = (-0.5 - 1.5)/2 = -2/2 = -1 - не удовл. ОДЗ

Ответ: x=1/2

Answer 2

To solve the equation lg(0.5 + x) + lg(x) = lg(0.5), you can use logarithmic properties to simplify and solve for x. Here's the step-by-step process:

1. Apply the logarithmic property log_a(b) + log_a(c) = log_a(b * c):

lg(0.5 + x) + lg(x) = lg(0.5) lg((0.5 + x) * x) = lg(0.5)

2. Remove the logarithms by taking the antilog (base 10):

(0.5 + x) * x = 0.5

3. Expand the equation by multiplying both sides by 2 to get rid of the decimal:

2(0.5 + x) * 2x = 2(0.5)

1 + 2x = 1

4. Subtract 1 from both sides of the equation:

2x = 0

5. Divide both sides by 2 to solve for x:

x = 0

So, the solution to the equation lg(0.5 + x) + lg(x) = lg(0.5) is x = 0.