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PSAT Math : Algebra

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #2 : 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 #5 : Exponents And Rational Numbers

$\log 3=a$

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

If a piece of pie is cut into 3 sections, and each of those pieces is further cut into three sections, then those pieces are cut into three sections, how many (tiny) pieces of pie are there?

Possible Answers:

125

Correct answer:

Explanation:

The answer is 3³ = 27

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

Solve for .

$\log _{9}x=\frac{1}{2}$

Possible Answers:

Correct answer:

Explanation:

$\log _{9}x=\frac{1}{2}$

$x = 9^{\frac{1}{2}}= 3$

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

$Simplify: \frac{\sqrt[3]{81}}{\sqrt[3]{3}}$

Possible Answers:

$\sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

$\sqrt[3]{81\star 3}= \sqrt[3]{243} = 6.24$

$\frac{81}{3}= 27$

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \frac{3}{1}= 3$

$\frac{\sqrt[3]{9\star 9}}{\sqrt[3]{9}}= \sqrt[3]{9}$

Correct answer:

$\sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

Explanation:

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

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

Rationalize the denominator:

$\frac{1}{2-\sqrt{3}}$

Possible Answers:

$\sqrt{3}$

$2+\sqrt{3}$

$2-\sqrt{3}$

$\frac{2+\sqrt{3}}{7}$

Correct answer:

$2+\sqrt{3}$

Explanation:

The conjugate of $2-\sqrt{3}$ is $2+\sqrt{3}$ .

Now multiply both the numerator and the denominator by $2+\sqrt{3}$

and you get:

$\frac{2+\sqrt{3}}\left ({2-\sqrt{3}} \right )\left ( 2+\sqrt{3} \right )$

$\left ( 2-\sqrt{3} \right )\left ( 2+\sqrt{3} \right ) =2^{2}-\left ( \sqrt{3} \right )^{2} =4-3 = 1$

Hence we get

$\frac{2+\sqrt{3}}{1} = 2+\sqrt{3}$

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Example Question #11 : Exponential Ratios And Rational Numbers

Solve for :

$3^{x-5} = \frac{1}{27}$

Possible Answers:

Correct answer:

Explanation:

$3^{x-5}=\frac{1}{27}=3^{-3}$

x-5=-3

x=2

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Example Question #4 : How To Find A Rational Number From An Exponent

Solve for .

$\log _{5}x=2$

Possible Answers:

125

Correct answer:

Explanation:

$log_5{x} = 2$

$x = 5^{2} = 25$

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Example Question #5 : How To Find A Rational Number From An Exponent

If,

$log_a{120}= log_b{120}$

What does a=?

Possible Answers:

a=b

$\frac{a}{b}= 120$

a=10

b=10

ab=10

Correct answer:

a=b

Explanation:

If $log_a{x} = log_b{x}$ ,

then a=b .

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PSAT Math : Algebra

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

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

Example Question #5 : Exponents And Rational Numbers

Example Question #6 : Exponents And Rational Numbers

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 A Rational Number From An Exponent

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

Example Question #11 : Exponential Ratios And Rational Numbers

Example Question #4 : How To Find A Rational Number From An Exponent

Example Question #5 : How To Find A Rational Number From An Exponent

All PSAT Math Resources

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