If g(x = log subscript 7 x then what is the value of g(1/49)? I believe it's 1/2 but I'm not sure.
no
recall that log 1/49 (base7) = log 1 - log 49
= 0 - 2
=-2
To find the value of g(1/49), we need to substitute 1/49 into the function g(x) = log base 7(x).
First, let's simplify the logarithm expression log base 7(1/49):
log base 7(1/49) = log base 7(1) - log base 7(49)
Since log base b(1) = 0 for any base b, the first term simplifies to 0:
log base 7(1) = 0
For the second term, we can simplify it further by using the property log base b(x^y) = y * log base b(x). In this case, we have:
log base 7(49) = log base 7(7^2) = 2 * log base 7(7)
Using the property log base b(b) = 1, we can simplify the expression further:
log base 7(7) = 1
Now, substituting the simplified expressions back into the original logarithm expression, we have:
log base 7(1/49) = 0 - 2 * 1 = 0 - 2 = -2
Therefore, g(1/49) = -2, not 1/2.