log1/5(1/125)=x?

Question

i'm not sure how to do this
so it becomes... 1/5^x=1/125? now i'm lost...

Answer 1

it goes dis way

(1/5)^x = (1/125)
=> (1/5)^x = (1/5)^3 since 5^3 = 125
=> x = 3. comparin both sides.

Answer 2

log[base 1/5] (1/125) = x

Your first step is to convert this to logarithmic form. That is,
log[base b](c) = a is the same as b^a = c.

(1/5)^x = (1/125)

Note that 1/5 is the same at 5^(-1), so we have

[5^(-1)]^x = 1/125

Also, note that 125 = 5^3.

[5^(-1)]^x = 1/5^3

1/5^3 is the same as 5^(-3)

[5^(-1)]^x = 5^(-3)

The exponential property (a^b)^c = a^(bc) applies here.

5^(-x) = 5^(-3)

Now that we have the same base on both sides, equate the powers.

-x = -3
Therefore
x = 3.

Answer 3

log base 1/5 of 1/125 equals x, so using the scorpion tail method, they are asking 1/5 raised to the x power equals 1/125, so the answer is 3

Answer 4

x = log[base 1/5] (1/125) = log[base 1/5] (1/5^3)
x = log[base 1/5] {(1/5)^3} = 3

x = 3

Answer 5

log(1/5)(1/125) = x

(1/5)^x = (1/125)

You can also write this as

5^x = 125

5^x = 5^3

x = 3

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The best way to do this on a calculator is

log(1/5)(1/125) =
(log(1/125))/(log(1/5)) =
(log(125^-1))/(log(5^-1)) =
(-log(125))/(-log(5)) =
(log(125))/(log(5)) =
3

Answer 6

1/5^x=1/125
1/5^x=1/5^3
Now compare both sides and you will get
x=3