## geerky42 Group Title $$\large b^x = b^y \Rightarrow x = y$$ iff $$\large b > 0, b \neq 1$$ Why b>0? Why not b ≠ 0? one year ago one year ago

1. freckles Group Title

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

2. geerky42 Group Title

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

3. freckles Group Title

-1 is smaller than 0

4. freckles Group Title

The statement did not work for b<0

5. geerky42 Group Title

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

6. geerky42 Group Title

except -1...

7. geerky42 Group Title

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

8. freckles Group Title

Is the the thingy suppose to go both ways?

9. freckles Group Title

Or do you mean it just in that one way?

10. geerky42 Group Title

Well, both way, I guess.

11. geerky42 Group Title

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

12. freckles Group Title

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

13. freckles Group Title

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

14. freckles Group Title

15. freckles Group Title

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

16. freckles Group Title

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

17. freckles Group Title

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

18. geerky42 Group Title

Well, this makes sense. Thanks.