PSAT Math : Exponential Ratios and Rational Numbers

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #531 : Algebra

If  and are positive integers and , then what is the value of ?

Possible Answers:

Correct answer:

Explanation:

43 = 64

Alternatively written, this is 4(4)(4) = 64 or 43 = 641.

Thus, m = 3 and n = 1.

m/n = 3/1 = 3.

Example Question #1 : How To Find A Ratio Of Exponents

Write the following logarithm in expanded form:

 

Possible Answers:

Correct answer:

Explanation:

Example Question #231 : Exponents

Com_exp_1

Which of the following lists the above quantities from least to greatest?

Possible Answers:

II, III, I, IV

I, III, II, IV

IV, III, II, I

I, IV, II, III

I, IV, III, II

Correct answer:

I, III, II, IV

Explanation:

Com_exp_2

Com_exp_3

Example Question #1 : Exponents And Rational Numbers

Solve for .

2^{x}= 64

Possible Answers:

Correct answer:

Explanation:

Since 2^{x}= 2^{6}

Hence

Example Question #2 : Exponents And Rational Numbers

Simplify:

 

Possible Answers:

Correct answer:

Explanation:

Example Question #3 : Exponents And Rational Numbers

Solve for :

Possible Answers:

Correct answer:

Explanation:

From the equation one can see that

Hence  must be equal to 25.

Example Question #4 : Exponents And Rational Numbers

Evaluate:

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : Exponents And Rational Numbers

Solve for .

 

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Exponents And Rational Numbers

and

 

Find

Possible Answers:

Correct answer:

Explanation:

Hence the correct answer is .

Example Question #1 : How To Find An Exponent From A Rational Number

Solve for .

Possible Answers:

Correct answer:

Explanation:

Use the rules of logarithms to combine terms.

Hence,

By fatoring we get

Hence .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

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