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Subject Test Math 1

Question 17 of 32

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SAT Subject Test

If log function application subscript c end subscript a equals x, which of the following must be true?

Select an Answer

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

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 equals log function application subscript c end subscript a invisible times, so c to the power of x end exponent equals c to the power of log function application subscript c end subscript a end exponentmust be true. One of the laws of logarithms states that c to the power of log function application subscript c end subscript a end exponent equals a must be true. Therefore, c to the power of x end exponent equals 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 function application subscript c end subscript a invisible times, is the exponent to which the base c must be raised to obtain a. In other words, x equals log function application subscript c end subscript a invisible times means precisely that c to the power of x end exponent equals a.

Question Difficulty: 
medium