Question

If 6^ = 1/126 find the value of x Please ask help with b

Answer 1

9514 1404 393

Answer:

  a) x = -3

  b) 1/250

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

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a) It is helpful to know that 216 = 6^3.* Then you would realize that ...

  $6^x=\dfrac{1}{216}=\dfrac{1}{6^3}=6^{-3}\\\\x=-3$

If you don't know that, then you can solve the equation using logarithms. Taking the log of both sides, you have ...

  x·log(6) = log(1/216)

  x = log(1/216)/log(6) = -3

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b)

  $5^{-3}\times 2^{-1}=\dfrac{1}{5^3}\times\dfrac{1}{2^1}=\dfrac{1}{125}\times\dfrac{1}{2}=\boxed{\dfrac{1}{250}}$

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* This would be on your list of cubes of small integers that you might want to memorize, along with squares of numbers less than 20.