The logarithmic equation y = log_b(x) passes through the point (1/6, - 1) . What is the value of b?

Answer 1

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.