## anonymous 5 years ago solve for x: log base 8(x+1)=2/3

1. anonymous

so you'll rewrite that as (the third root of 8) or 2, then square that = x + 1 2^2 = 4 = x + 1 so x = 3

2. anonymous

maybe i didnt write it right but its log small 8 (x+1)=2/3 can you explain how to solve that?

3. anonymous

the (x+1) is not small right? and it's on the same line as Log?

4. anonymous

yeah only the 8 is smaller and a line below the log

5. anonymous

Yeah I explained it above

6. anonymous

do you move the 8 to the right and put it to the 2/3?

7. anonymous

The formula is: [a ^{k} = x and that can be written as Log base a of x = k

8. anonymous

i dont understand how to show my steps

9. anonymous

In general, $\log_{a}c = b \ \ , a^{b} = c$

10. anonymous

So your is Log base 8 of (x + 1) = 2/3 Therefore it's: 8^(2/3) = x + 1 8 ^ (2/3) = The third root of 8 ( or 2), then you square it ( or 4)! So you have 4 = x + 1 So x = 3 And yes, that's the same one except it's using a,b, and c instead! ^^

11. anonymous

$\log_{8} x+1 = \frac{2}{3} \ \ , 8^{\frac{2}{3}} = x+1$ $8^{\frac{2}{3}} = (\sqrt[3]{8})^2 = 2^2 = 4$ $4 = x+1 \ \ , x = 3$ Sorry if I'm invading, HanhLive; just formatting it so it's easier to read :)

12. anonymous

okk thank you i got it