# Thread: Couple questions involving continuity and logarithms....

1. ## Couple questions involving continuity and logarithms....

#1. show that the given equation has at least one solution on the indicated interval.

tanx=2x^2-1 on (-pi/4,0)

I tried pluggin in -pi/4 and i got pi^2/8... now what?

#2. Find a and b

f(x) = tan(ax) if -pi/2<ax<0, -pi/2<bx<0

4 if x=0

ax+b if x>0

... i dont even know how to begin this one...

#3. exp(log base e 25)

i know that that is e^(log base e 25), but i dont know how to solve it after that...

#4. log base2 (X^(log base2 X))=4

so 16=x^(log base2 X)... but then what do i do?

Thank You,
Diggidy

2. 1. Plug in x = 0, what sign does it have?
If f(x) is continuous, f(a) < 0 but f(b) > 0 then f(x) must cross the x-axis.

2. Is f(x) continuous? If yes then f(x) as x->0 = f(0)

3. Let m = exp(log base e 25)
Take log of both sides on base e. What is m?

4. log base2 (X^(log base2 X))=4
X^(log base2 X) = 16
If y = log base 2 X, what is X in terms of Y? Put that in the equation.