Exponential Functions

Exponential Functions: Level 3 Challenges


916x2 \Huge \sqrt{\color{#D61F06}9^{\color{#20A900}{16} \color{#3D99F6}{x^2}}}

Which of the following is equal to the above expression?

A=25555,B=33333,C=62222 \large A = 2^{5555}, \qquad B = 3^{3333}, \qquad C = 6^{2222}

What is the order of these numbers from smallest to largest?

If 2x=3y=6, 2^x = 3^y = 6, then which of the following statements is true?

Find the sum of all integer solutions to the equation

(x23x+1)x+1=1.\large (x^2 - 3x + 1)^{x + 1} = 1.

If you have a piece of paper that is 0.1 mm0.1\text{ mm} thick, then how many times will you have to fold it in half in order for it to become tall enough to reach the moon?

Note: The distance from the earth to the moon is 384400 km 384400\text{ km}.

You have to round off the answer that you are getting to get the answer that you will enter in the answer box.


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