Question

Solve exactly.
log(base 5)(x+1) = log(base 5)(3-x)
X= ?

Answer 1

Since you have the same bases, you can just set x + 1 = 3 - x and solve for x.

Answer 2

so x = 1?

Answer 3

Or even more generally. For any one-to-one function: \(f(a) = f(b) \implies a = b\)

Answer 4

Correct. x = 1

Answer 5

because the log bases are the same?

Answer 6

Because the log bases are the same, the output of the logs being equal means the inputs must be equal.

Answer 7

so for log(base 6)(x+1) + log(base 6)(x+2) = 1

Answer 8

would equal out to (x+1) = 1-(x+2) ?