Question

Pls solve if u can <3 much appreciated

Answer 1

Explanation:

that is only possible, if we don't need to use a 2 and a 5 (but especially the 2) to create the 1 in the middle (log(10) = log(2×5) or log (5×2) = 1).

in other words, if the 1 in the middle is just a given, and does not use any of our digits for is creation, then a solution is possible.

first of all, the upper left corner has to be log(0⁰). we cannot use the digit 0 for anything else. and 0^n (except for n = 0) is not a valid argument for a logarithm.

log(0⁰) = 0 log(2×1) = 0.3... log(9/4) = 0.35...

log(1×2) = 0.3... 1 log(3×6) = 1.26...

log(7/3) = 0.37... log(4×5) = 1.3... log(6⁹) = 7.0...

but as soon as we need to build the center 1 by log(10), which takes then away one of the 2s (as the only way to build 10 by multiplication is 2×5 or 5×2), there is no possible solution.

Answer 2

Please see attachment.

Explanation:

There are many possible solutions to this problem.

A few things to note:

• 
  `\log_a1=0`
• The log of a number smaller than its base is less than 1.
• The log of a number larger than its base is more than 1.
• 
  `\log_a0\:\:\textsf{is und\;\!efined}`

There are 8 red boxes and 8 blue boxes, so we do not have to use every digit from 0 to 9.

Place zero in the blue box in the top left of the grid, since any number raised to zero is 1 and
`\log_a1=0`. Leave the red box blank for the moment, and fill it with any number not used at the end.

The value of the product of the red and blue boxes in the top-middle and left-middle of the grid should be less than 10. It is advisable to place the lowest numbers in these boxes, i.e. 1 and 2.

The value of the product of the red and blue boxes in the bottom-middle and right-middle of the grid should be more than 10.

It is advisable to place some of the highest numbers in the bottom right corner of the grid, as this is the box with the greatest value.

Please see the attached image for one possible way of filling the grid. The actual values of the logarithms (to 3 decimal places) have been placed in the bottom right corners of each box of the grid for verification.