SOLUTION: Hello! I need help solving 2 equations involving Logarithms. How do I correctly graph the equation bellow on the same coordinate plane? Question #1: F(x)= 2^-x and G(x)= 4^x

Question 627566: Hello! I need help solving 2 equations involving Logarithms.
How do I correctly graph the equation bellow on the same coordinate plane?
Question #1: F(x)= 2^-x and G(x)= 4^x
Question #2:
How do I solve/or rewrite this equation as a single quantity?
log^2 (x) + log^2 (x+2) = log^2 (x +6)
Please help me! LOL
-Cass
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Hello! I need help solving 2 equations involving Logarithms.
How do I correctly graph the equation bellow on the same coordinate plane.
..
Question #1: F(x)= 2^-x and G(x)= 4^x
..
For F(x)=2^-x=1/2^x
Domain: (-∞,∞)
Range: (0,∞)
Horizontal asymptote: x-axis or y=0
..
For F(x)=4^x
Domain: (-∞,∞)
Range: (0,∞)
Horizontal asymptote: x-axis or y=0
See graph below: Green curve is 4^x and red curve is 2^-x or 1/2^x
Note that both curves have a y-intercept=1 (2^0=1)
Also note both functions are always >0
..
Question #2:
How do I solve/or rewrite this equation as a single quantity?
log^2 (x) + log^2 (x+2) = log^2 (x +6)
log^2[ (x) (x+2)] = log^2 (x +6)
x(x+2)=x+6
x^2+2x=x+6
x^2+x-6=0
(x+3)(x-2)=0
x=-3 (reject, x>0)
or
x=2

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