Otilio Guerra

Lv 4

# Logarithm Help?

Question: If log[b]4=k, then log[b]16=?

Answer: 2k

I had it last night but know I forgot how the algorithm for this problem and I would appreciate any sort of help.

### 2 Answers

Relevance

- 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

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