Question

Which pair of equations is not equivalent?

log₂ (16) = 4 and 24 = 16
O
3² = 9 and log3 (9) = 2
○ log₂ (6) = − 4 and 4-² =
16
O
1
16
=
1
10¹ and log(0.1) = -1
10

Answer 1

Answer: Choice C

Reason:

The bases for the 1st and 2nd expression are 2 and 4 respectively. The bases do not match, which is why the expressions aren't equivalent for choice C.

The general template is
`\text{y} = b^{\text{x}} \ \text{ is equivalent to } \ \log_(b)(\text{y}) = \text{x}` where both bases are "b". This transformation is useful to help isolate the exponent.

Choice A is a valid example of where we go from log form to exponential form, or vice versa. Take note the bases are the same here (both 2).

Choice B is also valid since the bases are 3 each.

Choice D is valid as well. Writing "log" without a stated base has us assume the default of base 10. The fraction 1/10 is equivalent to the decimal form 0.1