Question

Log^5 (5-x)=2 log^5 3

Answer 1

Если 5 имеется ввиду основание,то
5-x=3^2
5-x=9
x=5-9
x=-4
из одз: 5-x>0; x<5
Ответ удовлетворяет одз

Answer 2

To solve the equation log^5(5-x) = 2 log^5(3), you can use logarithmic properties to simplify it. First, remember that log^a(b) = log^c(b) is equivalent to b = c, where a and c are the bases of the logarithms. In this case, both sides of the equation have the same base (log base 5), so you can equate the expressions inside the logarithms:

5 - x = 3^2

Now, simplify the right side:

5 - x = 9

To isolate x, you can subtract 5 from both sides of the equation:

-x = 9 - 5

-x = 4

Now, to solve for x, multiply both sides by -1 (or you can also think of it as taking the negative of both sides):

x = -4

So, the solution to the equation log^5(5-x) = 2 log^5(3) is x = -4.