evaluate the logarithm log 5 1/625

log 5 1/625

= log5 625^-1
= log5 5^-4
= -4log5 5
= -4

To evaluate the logarithm log5 (1/625), we need to determine what power of 5 gives us 1/625.

Since 5^4 = 625, we can rewrite 1/625 as 5^(-4).

Therefore, log5 (1/625) = -4.

So, the value of the logarithm is -4.

To evaluate the logarithm log5 (1/625), we can use the definition of logarithm. The logarithm of a number to a given base is the exponent to which the base needs to be raised to obtain that number.

In this case, we want to know the exponent to which the base 5 needs to be raised to obtain 1/625. To solve this, we can rewrite 1/625 as a power of 5.

1/625 can be written as 5^(-4) because 5^(-4) = 1 / (5^4) = 1/625.

So, the logarithm log5 (1/625) can be simplified to log5 (5^(-4)), which is the same as -4.

Therefore, log5 (1/625) = -4.