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.