## anonymous one year ago log{b} 1000=3 I know b=10 but I don't understand how they got there.

1. anonymous

$\log_{b} 1000=3$

2. anonymous

$b^3=1000$ $3\sqrt{b^3}= 3\sqrt{1000}$ b=10

3. Nnesha

well did you take 3rd root right ? you can write 1000 in terms of 3 exponents

4. Nnesha

x^3 =1000 ? what is x

5. anonymous

10

6. anonymous

What is the point of the 3's in front of the square root signs?

7. Nnesha

that's not 3 it's a 3rd rooot i guess like this $\huge\rm \sqrt[3]{b^3}$

8. anonymous

Right, I didn't know how to do that

9. Nnesha

you can convert 3rd to 1/3 exponent $\huge\rm \sqrt[3]{b^3} = b^{3 \times \frac{ 1 }{ 3 }}$ so cancel out 3 exponent u have to take 3rd root :=)

10. Nnesha

$\huge\rm \sqrt[3]{b^3} = b^{\cancel3 \times \frac{ 1 }{\cancel 3 }}=b$

11. anonymous

Wouldn't that also mean that 1000 would be multiplied by 1/3?

12. Nnesha

yes so 1000 can be written as 10 to the 3rd power $\huge\rm \sqrt[3]{10^3}$

13. anonymous

See that's where I get confused, so the 1000 get simplified down to 10 because?

14. Nnesha

because it's easy to solve without calculator and it's legal :3

15. anonymous

-_- so because 10^3=1000 it gets simplified to 10^3 and since it's the 3rd root the exponent cancels out leaving b=10 ?

16. Nnesha

b to the 3rd power so you can either write 10 to the 3rd power or put 3rd root of 1000 into the calculator :=)

17. Nnesha

yep

18. anonymous

See when I enter that into my calc I get 94.86....

19. Nnesha

and it's helpful when you have to find an exponent given base for example 10^x = 1000

20. Nnesha

what did you enter ?

21. freckles

$3 \sqrt{1000} \neq \sqrt[3]{1000}$

22. anonymous

$3\sqrt{1000}$

23. anonymous

Yea see I don't know how to enter the latter

24. Nnesha

it's not 3 times square root of {1000} 3rd root like $\sqrt[3]{1000}$

25. Nnesha

ohh then convert 3rd root to 1/3 exponent $\huge\rm \sqrt[3]{1000} = (1000)^\frac{ 1 }{ 3 }$

26. anonymous

That works. =] Could you possibly help me with another problem?

27. Nnesha

gtg :3 sorry

28. anonymous

All's well Thank you for your help :)

29. Nnesha

my pleasure