Question

The expression mc001-1.jpg is the result of applying the change of base formula to a logarithmic
expression. Which could be the original expression?

mc001-2.jpg

mc001-3.jpg

mc001-4.jpg

mc001-5.jpg

Answer 1

I can’t see the images — could you retype the expression that resulted from the change-of-base and the four answer choices (or upload the images again)?

While you do that, here is the quick method so you can check yourself:

- The change-of-base formula is
log_b(A) = log_k(A) / log_k(b)
for any convenient base k (often 10 or e).
- So when you see a fraction of two logs with the same log-type (same base) — e.g. ln(5)/ln(2) or log(5)/log(2) — it is equal to log base (denominator’s argument) of (numerator’s argument):
ln(5)/ln(2) = log_2(5).
- If the numerator or denominator is a sum or difference use log laws first: e.g.
(ln7 + ln3)/ln2 = ln(21)/ln2 = log_2(21).
(log8 − log2)/log4 = log(8/2)/log4 = log_4(4) = 1.

So paste the fraction you have (or the four choices) and I’ll point which original expression matches.