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Hey... requested my professor to give me a few questions to enable me to improve my skills... am having problems solving them however and was hoping that you could guys could help me:

Q1) Use a calculator to evaluate the following powers. Round the results to five decimal placeS. Each of these powers has a rational exponent. Explain how you can use these powers to define 3^( sqrt of 2 ) which has an irrational exponent.

3^(14/10) = 4.65554

3^(141/100)=4.70697

3^(1414/10000)= 4.72770

3^(14142/10000)= 4.72873

3^(141421/100000)= 4.72878

3^(1414213/1000000)= 4.72880

3^( sqrt of 2 ) = 4.728804

so basically the value of 3^(sqrt of 2 ) comes after 3^(1414213/1000000)... hence, you could find the log of 3^14/10 which is .6679697566, then probably do the following : 3^(.667..+.667...+.667....+.667.. +.667 +.667.. +.667).

EDIT: damn .. what i did above doesnt make sense.. im soo confused.!!! i do know that i can somehow use logs by finding the log of one value and then adding the solution multiple times to find the value of 3^ ( sqrt of 2 )

EDIT 2: realized that i posted in wrong forum.. my bad.. shall post in general math forum...

Q1) Use a calculator to evaluate the following powers. Round the results to five decimal placeS. Each of these powers has a rational exponent. Explain how you can use these powers to define 3^( sqrt of 2 ) which has an irrational exponent.

3^(14/10) = 4.65554

3^(141/100)=4.70697

3^(1414/10000)= 4.72770

3^(14142/10000)= 4.72873

3^(141421/100000)= 4.72878

3^(1414213/1000000)= 4.72880

3^( sqrt of 2 ) = 4.728804

so basically the value of 3^(sqrt of 2 ) comes after 3^(1414213/1000000)... hence, you could find the log of 3^14/10 which is .6679697566, then probably do the following : 3^(.667..+.667...+.667....+.667.. +.667 +.667.. +.667).

EDIT: damn .. what i did above doesnt make sense.. im soo confused.!!! i do know that i can somehow use logs by finding the log of one value and then adding the solution multiple times to find the value of 3^ ( sqrt of 2 )

EDIT 2: realized that i posted in wrong forum.. my bad.. shall post in general math forum...

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