How do you solve:

log (1/3) 1 ?

let z = log(1/3) 1

(1/3)^z = 1

z = 0 because (1/3)^0 = 1

so
log(1/3)1 = 0

in fact log to any base of 1 is zero

To solve the expression log(base 1/3)1, we need to understand how logarithms work.

The logarithm of a number represents the exponent to which a base must be raised to obtain that number. In this case, the base is 1/3, and we want to find the exponent that gives us 1.

In other words, we need to find x such that (1/3)^x = 1.

To solve for x, we can rewrite the equation using exponent rules. Recall that any number raised to the power of 0 is equal to 1:

(1/3)^x = (1/3)^0

Since both sides have the same base, we can equate the exponents:

x = 0

Therefore, the solution to log(base 1/3) 1 is 0.