- #1

dfklajsdfald

- 10

- 0

## Homework Statement

the point (log a, log b) exists on the unit circle. find the value of axb. round to the nearest thousandths.

## Homework Equations

x

^{2}+ y

^{2}= 1

## The Attempt at a Solution

x2+y2 = 1

loga

^{2}+logb

^{2}=1

2loga+2logb = 1

2(loga+logb) = 1

loga + log b = 0.5

logb = 0.5−loga

now i try and subsitute logb in

loga

^{2}+(0.5−loga)

^{2}= 1

when i did this it wouldn't work after the last step. so this is what i tried next

(loga)

^{2}+ (log b)

^{2}= 1

loga = √1-(logb)

^{2}

then i did

(√1-(logb)

^{2})

^{2}+ (logb)

^{2}= 1

1-(logb)

^{2}= 1-(log b)

^{4}

-(logb)

^{2}+ (logb)

^{4}= 0

factored out (logb)

^{2}so i got

1 = logb

and 10

^{1}= b so b = 10 but I am not sure if that's right either because it seems iffy to me

i think i was on the right track with the first one but idk can someone help please