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PSAT Math : Exponential Ratios and Rational Numbers

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Example Questions

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

If and are positive integers and , then what is the value of $\frac{m}{n}$ ?

Possible Answers:

$\frac{5}{3}$

$\frac{1}{3}$

$\frac{1}{16}$

Correct answer:

Explanation:

4³= 64

Alternatively written, this is 4(4)(4) = 64 or 4³= 64^1.

Thus, m = 3 and n = 1.

m/n = 3/1 = 3.

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Example Question #2 : How To Find A Ratio Of Exponents

Write the following logarithm in expanded form:

$\log x^{2}y$

Possible Answers:

$2\log x+\log y$

$\log x^{2}+\log y$

$\log x+\log y$

$2\left ( \log xy \right )$

$2\log x-\log y$

Correct answer:

$2\log x+\log y$

Explanation:

$\log x^{2}y=\log x^{2}+\log y=2\log x+\log y$

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Example Question #2 : Exponents And Rational Numbers

Com_exp_1

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

Possible Answers:

II, III, I, IV

I, IV, II, III

I, IV, III, II

I, III, II, IV

IV, III, II, I

Correct answer:

I, III, II, IV

Explanation:

Com_exp_2

Com_exp_3

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

Solve for .

$2^{x}= 64$

Possible Answers:

x=-6

x=64

x=5

x=6

$x=64^{2}$

Correct answer:

x=6

Explanation:

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

Hence x=6

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

Simplify:

$\sqrt[3]{x^{10}y^{8}z^{9}}$

Possible Answers:

$x^{3}y^{3}z^{3}$

$\sqrt[3]{xy^{2}}$

$x^{3}y^{2}z^{3}^{\sqrt[3]{xyz}}$

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

$x^{3}y^{2}z^{3}$

Correct answer:

$x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

Explanation:

$\sqrt[3]{x^{9}xy^{6}y^{2}z^{9}}=x^{3}y^{2}z^{3}\sqrt[3]{xy^{2}}$

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

Solve for :

$\sqrt{x} -1= 4$

Possible Answers:

Correct answer:

Explanation:

From the equation one can see that

$\sqrt{x} = 5$

Hence must be equal to 25.

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Example Question #2 : How To Find An Exponent From A Rational Number

Evaluate:

$\log 0.1=$

Possible Answers:

$\frac{1}{10}$

Correct answer:

Explanation:

$0.1= 10^{-1}$

$\log 0.1=-1$

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

Solve for .

$\log_{2}x=4$

Possible Answers:

Correct answer:

Explanation:

$x= 2^4{}= 16$

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Example Question #3 : How To Find An Exponent From A Rational Number

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

Possible Answers:

a+b

$b^{2}$

$a^{2}$

Correct answer:

a+b

Explanation:

$\log 15=\log (5\cdot 3)=\log 5+\log 3$

Hence the correct answer is a+b .

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Example Question #2 : Exponents And Rational Numbers

Solve for .

$\log (x+3)+\log x=1$

Possible Answers:

$5\ or\ -2$

$-5\ or\ 2$

Correct answer:

Explanation:

Use the rules of logarithms to combine terms.

$\log (x(x+3))=1$

Hence, $x(x+3)=10^{1}$

$x^{2}+3x=10$

x^2+3x-10=0

By fatoring we get (x+5)(x-2)=0

Hence $x=-5\ or\ 2$ .

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

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PSAT Math : Exponential Ratios and Rational Numbers

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

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

Example Question #2 : How To Find A Ratio Of Exponents

Example Question #2 : Exponents And Rational Numbers

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

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

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

Example Question #2 : How To Find An Exponent From A Rational Number

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

Example Question #3 : How To Find An Exponent From A Rational Number

Example Question #2 : Exponents And Rational Numbers

All PSAT Math Resources

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