$\large b^x = b^y \Rightarrow x = y $ iff $\large b 0, b \neq 1$

Why b0? Why not b ≠ 0?

Question

$\large b^x = b^y \Rightarrow x = y $ iff $\large b > 0, b \neq 1$

Why b>0? Why not b ≠ 0?

freckles · Answer

(-1)^3=(-1)^5 =>  3=5.
True or false?

geerky42 · Answer

Ok, how about b≠-1, 0, 1?

I just don't understand why b couldn't be smaller than zero...

freckles · Answer

-1 is smaller than 0

freckles · Answer

The statement did not work for b<0

geerky42 · Answer

except -1... Why couldn't it be smaller than zero?

geerky42 · Answer

except -1...

geerky42 · Answer

Why not $b \in \mathbb{R}, b \neq -1, 0, 1$?

freckles · Answer

Is the the thingy suppose to go both ways?

freckles · Answer

Or do you mean it just in that one way?

geerky42 · Answer

Well, both way, I guess.

geerky42 · Answer

I found this statement in a iPhone app called Math Formulas, I think this is wrong, but I'm not sure...

freckles · Answer

Well it is probably leading up to logarithms...
Of course 1^n=1^m but this does not imply n=m.

freckles · Answer

Oh you understand why b cannot be -1,0, or 1.

freckles · Answer

Have you talked about logarithms?

freckles · Answer

$$\log_b(x)=\frac{\ln(x)}{\ln(b)} , x>0, b>0, b \neq 1$$

freckles · Answer

$$b^x=b^y$$
$$\log_b(b^x)=\log_b(b^y)$$
$$x \log_b(b)=y \log_b(b)$$
$$x(1)=y(1)$$
$$x=y$$

freckles · Answer

That is assuming b>0 and b does not equal 1.

geerky42 · Answer

Well, this makes sense. Thanks.