i keep forgetting?

Question

how do you do--- .5 = .8 to the X power
how do you find x

Answer 1

There are multiple ways to do this, but here's my way...
First, get the concept:
If
x^2 = 4
Then
log(base x)4 = 2

So, use this same procedure to change the exponents to a logarithm.

.5 = .8^x
log(base .8).5 = x
Then, use the calculator to solve.
This would be (log .5)/(log .8)
So, the answer is 3.1063...

If you plug it back in to check, it's the right answer.
.5 = .8^x
.5 = .8^3.1063
.5 = .49999
We rounded the answer, and because they are so close in proximity to each other, we assume that the answer would have been exact without the rounding. So, the answer 3.1063 is correct.

--I'm not sure how many decimal places you're instruct to round to though. My teacher just always wanted four...

Answer 2

try taking log of both sides

log .5 = log (.8) ^ x

then

log .5 = x log (.8)
x = log .5 / log .8
and use calculator

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For Logarithm Rules, see also
http://www.sosmath.com/algebra/logs/log4/log44/log44.html

Answer 3

ln(.5)/ln(.8) = 3.10628372
Then to check your answer:
.8^(3.10628372) = .5