anonymous 4 years ago solve. then round answer to the nearest hundredth. log_5x=3

1. anonymous

@dpflan ?

2. anonymous

$log_5x=3$Is that the equation?

3. anonymous

yess

4. anonymous

$log_ab=x$ OK, this means, the number you raise a to in order to obtain x is b. so $a^x = b$

5. anonymous

ok..

6. anonymous

would it be x = 5^3 = 125?

7. anonymous

$log_5x=3$ Is $5^3 = x$... Yeah you got it

8. anonymous

what is 125 to the nearest..?

9. anonymous

$125 = 125.00000...$

10. anonymous

just like the last one ;)

11. anonymous

what would 35 be rounded to the hundredth? 35.000?

12. anonymous

?

13. anonymous

Actually, no, you need one less 0. Using the decimal system, the values to the right of the decimal are fractional amounts with respect the base for the system, which is 10 here. So the first place would be $10^{-1}$ which is 1/10, the second place is $10^{-2}$ which is $\frac{1}{10^2}=\frac{1}{100}$ , this that is the "hundredths" place

14. anonymous

so just two points to the right would be to the nearest hundrdeth

15. anonymous

cool..it didnt have anything to do with the previous question..

16. anonymous

i just wanted to know what 35 rounded to the nearest hundredth would be

17. anonymous

It's actually kind of cool, you use any number as the base. So if you have 123.456, then you have $1*10^3 + 2*10^1 + 2*10^0 + 4*10^{-1} + 5*10^{-2} + 6*10^{-3}$

18. anonymous

At least in the decimal system

19. anonymous

is that for 35?

20. anonymous

No, 35 is 35.00