Question

Lg((x-5)в квадрате 2)=2

Answer 1

Ответ:

Объяснение:

lg(x-5)^2=2,  2lg|x-5|=2,  lg|x-5|=1,   |x-5|=10,  x-5=10,  x=15  или

x-5=-10,  x=-5,  по  ОДз  х-5>0,  x>5,  отв.  х=15

Answer 2

It seems like there might be a slight confusion in your equation notation. I'll try to interpret what you're asking. If you're trying to solve for the variable x in the equation:

lg((x - 5)^2) = 2

Here, "lg" likely represents the base-10 logarithm (common logarithm). The equation can be rewritten as:

log10((x - 5)^2) = 2

Now, the logarithmic equation can be transformed into an exponential form:

10^2 = (x - 5)^2

Solving for x:

100 = (x - 5)^2

Taking the square root of both sides:

±10 = x - 5

Adding 5 to both sides:

x = 5 ± 10

This gives two possible solutions for x:

1. x = 15
2. x = -5

However, when plugging these values into the original equation, you need to be careful with the domain of the logarithm. Logarithms are only defined for positive values, so the solution x = -5 is not valid in this context. Therefore, the only valid solution is:

x = 15