Answer:
x=2
Step-by-step explanation:
log_x(y)+log_x(z)=log_x(yz), so logb(x-1) + logb(x+2)=logb((x-1)(x+2)). next subtract logb(8-2x) from both sides to get logb((x-1)(x+2))-logb(8-2x)=0. log_x(y) - log_x(z) = log_x(y/z). so now we have logb((x-1)(x+2)/(8-2x)). now you can put it into exponential form: (x-1)(x+2)/(8-2x)=b^0=1 now just solve for x:
(x-1)(x+2)= 8-2x, x^2 + x -2 = 8-2x, x^2 + 3x -10 = 0, (x+5)(x-2)=0 x=-5, x=2. plug both into the original equation to check which one is correct, since log_x(y) can't have a negative y, x=-5 doesnt work
Answer:
B would be -7
Step-by-step explanation:
Because 6 times -7 equals -42
Answer:
Option C is correct.
Constant of variation k = -0.5
Step-by-step explanation:
The direct variation says that:
then, the equation is of the form: 
.....[1] where k is the constant of variation.
Given the table:
x f(x)=y
0 0
2 -1
4 -2
7 -3.5
Consider any values from the tables
x = 4 and y=f(x) = -2
Substitute these values in equation [1] we have;
Divide both sides by 4 we get;
Therefore, the constant of variation is, -0.5
