## anonymous 5 years ago log base 8 (0.25) compute the log

1. anonymous

-2/3

2. anonymous

You can think of it as => 8^(x) = 0.25? What does x need to be.

3. anonymous

you could also use change of base formula =ln(0.25)/ln(8)

4. anonymous

when i tried to solve it I broke it down to 8^y = 25/100. simplifed and got 8^y = 1/4. 2^3= 1/2^2. the i got stuck

5. anonymous

i know change of base works but i must show work

6. anonymous

8^x = 1/4 we know x has to be -, 8^(2/3) = 4

7. anonymous

Or if you're like me and you can never remember the change of base formula... Let $$k=log_8 (.25)$$ $\implies 8^k = .25$ $\implies k(ln8) = ln (.25)$ $\implies k = \frac{ln(.25)}{ln8}$ $\implies log_8(.25) = \frac{ln(.25)}{ln8}$

8. anonymous

8^2 = 64 third root of 64 = 4. The way you are showing you work if you can reason that.

9. anonymous

Ok I see