Question

Which of the following is equivalent to the expression log2⁡a=r? 2a = r logr⁡2 = a 2r = a log2⁡r = a

Answer 1

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Answer:

  (c)  2^r = a

Step-by-step explanation:

The relationship between log forms and exponential forms is ...

  $\log_2(a)=r\ \Leftrightarrow\ 2^r=a$

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Additional comment

I find this easier to remember if I think of a logarithm as being an exponent.

Here, the log is r, so that is the exponent of the base, 2.

This equivalence can also help you remember that the rules of logarithms are very similar to the rules of exponents.

Answer 2

Answer: Choice C)  $2^r = a$

This is the same as writing 2^r = a

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Explanation:

Assuming that '2' is the base of the log, then we'd go from $\log_2(a) = r$ to $2^r = a$

In either equation, the 2 is a base of some kind. It's the base of the log and it's the base of the exponent.

The purpose of logs is to invert exponential operations and help isolate the exponent. A useful phrase to help remember this may be: "if the exponent is in the trees, then we need to log it down".

The general rule is that $\log_b(y) = x$ converts to $y = b^x$ and vice versa.