Difference between revisions of "1956 AHSME Problems/Problem 8"
(Created page with "== Solution == Simple substitution yields <cmath>8 \cdot 2^{x} = 5^{0}</cmath> Reducing the equation gives <cmath>8 \cdot 2^{x} = 1</cmath> Dividing by 8 gives <cmath>2^{x}=\...") |
(→Solution) |
||
| Line 6: | Line 6: | ||
<cmath>8 \cdot 2^{x} = 1</cmath> | <cmath>8 \cdot 2^{x} = 1</cmath> | ||
Dividing by 8 gives | Dividing by 8 gives | ||
| − | <cmath>2^{x}=\frac{1 | + | <cmath>2^{x}=\frac{1}{8}</cmath> |
This simply gives that <math>x=-3</math> | This simply gives that <math>x=-3</math> | ||
| − | Therefore, the answer is <math>\fbox{(b) - | + | Therefore, the answer is <math>\fbox{(b) -3}</math> |
Revision as of 13:43, 31 August 2019
Solution
Simple substitution yields
![\[8 \cdot 2^{x} = 5^{0}\]](http://latex.artofproblemsolving.com/d/6/a/d6af6b14becb25e736b1d5508e3b4439c16d4091.png)
Reducing the equation gives
![\[8 \cdot 2^{x} = 1\]](http://latex.artofproblemsolving.com/0/0/2/0029b0b2a856bad4e423489d186011cd93e1c355.png)
Dividing by 8 gives
![\[2^{x}=\frac{1}{8}\]](http://latex.artofproblemsolving.com/8/a/4/8a40ad1d77235bf0f7ca675e0ebab1452efc7fde.png)
This simply gives that 
Therefore, the answer is 
