PLEASE HELP Explain how to solve 5x^(− 2) = 8 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

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  x ≈ 0.791

Step-by-step explanation:

You can divide by 5 to get the exponential factor by itself.

  x^(-2) = 8/5 = 1.6

Taking logarithms base x gives ...

Using the change of base formula, this can be rewritten to facilitate solution for x.

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Alternate solution

The equation can be solved without using logarithms at all.

  x^-2 = 8/5 . . . . divide by 5

  x^2 = 5/8 . . . . . invert both sides

  x = √(5/8) = √(10/16) = (√10)/4

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