2016 AMC 10A Problems/Problem 2: Difference between revisions
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==Solution== | ==Solution== | ||
We can rewrite <math>10^{x}\cdot 100^{2x}=1000^{5}</math> as <math>10^{5x}=10^{15}</math>. Since the bases are equal, we can set the exponents equal: <math>5x=15</math> | We can rewrite <math>10^{x}\cdot 100^{2x}=1000^{5}</math> as <math>10^{5x}=10^{15}</math>. Since the bases are equal, we can set the exponents equal: <math>5x=15.</math> Solving gives us: <math>x = \boxed{\textbf{(C)}\;3.}</math> | ||
==See Also== | |||
{{AMC10 box|year=2016|ab=A|before=First Problem|num-a=2}} | |||
{{MAA Notice}} | |||
Revision as of 18:23, 3 February 2016
Problem
For what value of 
does 
?
Solution
We can rewrite as 
. Since the bases are equal, we can set the exponents equal: 
Solving gives us: 
See Also
| 2016 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
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