Question: If log[b]4=k, then log[b]16=?
I had it last night but know I forgot how the algorithm for this problem and I would appreciate any sort of help.
- la consoleLv 71 month agoFavorite Answer
Log[b](4) = k → you know that: Log[a](x) = Ln(x) / Ln(a) ← where a is the base
Ln(4) / Ln(b) = k → you multiply by 2 both sides
2.Ln(4) / Ln(b) = 2k → you know that: x.Ln(a) = Ln(a^x)
Ln(16) / Ln(b) = 2k
Log[b](16) = 2k
- llafferLv 71 month ago
log_b(4) = k
You want to find out what log_b(16) is.
Let's call that x:
x = log_b(16)
So you want a value for x in terms of k.
Note that 16 is a power of 4, so:
x = log_b(4²)
We can pull the exponent out of the log to get:
x = 2 log_b(4)
And finally, substitute the variable k for the log expression:
x = 2k