.8^x=.0833

Question

I am wondering how to get x

Answer 1

The way I would do this is:

 

a^x = b

 

x = ln b / ln a

 

x = (ln .0833) / (ln .8)

 

That can be solved on the calculator.  I'm getting 11.138.  (A difference in intermediate rounding I'm sure.)

 

However, there's no way to know if they care which way you solve this.  But now you have two.

Answer 2

0.8^x = 0.0833

 

Take Natural Logarithms of both sides:

 

ln(0.8^x) = ln(0.0833)

 

Use Power Rule:

 

x ln(0.8) = ln(0.0833)

 

Solve for x and use calculator to find approximation:

 

x = ln(0.0833) / ln(0.8) ≈ 11.13770357768379

 

check on calculator:

 

0.8^(11.13770357768379) =? 0.0833

0.0833 = 0.0833 √

Answer 3

0.8^x=0.0833

log(0.8^x)=log(0.0833)

xlog(0.8)=log(0.0833)

x=log(0.0833)/log(0.8)

x=log(8.33*10^-2)/log(8*10^-1)

x=(0.9206-2)/(0.9031-1)

x=(-1.0794)/(-0.0969)

x=11.139319

check: 0.8^11.139319=0.0832699

Answer 4

.8^x = .0833

For exponential problems like this one, you can use logarithms to place the equation into a simple form more easily solved. Thus:.

log10(.8^x) =    xlog10(.8) Any base number can be used, even 0.8, but tables are available for log bases 2,                         e, and 10
= (-.0969)x       This can easily be obtained from a table of log values.
= log10(,0833)  Given by the problem.
= -1.079

X = -1.079/(-.0969) = 11.1352