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

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=(1)/(216)=(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)* 2^(-1)=(1)/(5^3)*(1)/(2^1)=(1)/(125)*(1)/(2)=\boxed{(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.