Subject Test Math 1

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Subject Test Math 1

Question 17 of 32

If $\log_{c} a = x$ , which of the following must be true?

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$a to the power of c equals x$

Correct Answer:

No

$a to the power of x equals c$

Correct Answer:

No

$c to the power of a equals x$

Correct Answer:

No

$c to the power of x equals a$

Correct Answer:

Yes

$x to the power of c equals a$

Correct Answer:

No

View Correct Answer

The correct answer is D.

One way to determine which equation must be true is to apply the laws of logarithms to the given equation. It is given that $x = \log_{c} a$ , so $c^{x} = c^{\log_{c} a}$ must be true. One of the laws of logarithms states that $c^{\log_{c} a} = a$ must be true. Therefore, $c^{x} = a$ must be true.

Alternatively, one can recall the definition of logarithms. The logarithm of $a$ to the base $c$ ,represented by the symbol $\log_{c} a$ , is the exponent to which the base $c$ must be raised to obtain $a$ . In other words, $x = \log_{c} a$ means precisely that $c^{x} = a$ .

Question Difficulty:

medium

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Subject Test Math 1

Question 17 of 32

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View Correct Answer