The logarithmic equation y = log_b(x) passes through the point (1/6, - 1) . What is the value of b?
To find the value of b, we substitute the point (1/6, -1) into the equation y = log_b(x).
-1 = log_b(1/6)
We know that log_b(1) = 0 for any value of b. So, we rewrite log_b(1/6) as:
log_b(1/6) = log_b(1) - log_b(6)
Now, we substitute log_b(1) = 0, log_b(6) = log(6)/log(b):
-1 = 0 - log(6)/log(b)
-1 = - log(6)/log(b)
Solving for b:
log(b) = log(6)
b = 6
Therefore, the value of b is 6.