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GRE Subject Test: Math : Algebra

Study concepts, example questions & explanations for GRE Subject Test: Math

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All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #151 : Algebra

$6 \times 3^{2y} = 216$

Possible Answers:

$y=\frac{\log_{3}(36)}{2}$

$y=\log_{36} (3)$

$y =\log_{3} (36)$

$y=\frac{\log_{36}(3)}{6}$

Correct answer:

$y=\frac{\log_{3}(36)}{2}$

Explanation:

$6 \times 3^{2y} = 216$

Divide both sides by

$3^{2y} = 36$

Write in logarithm form and solve for

$2y =\log_{3} (36)$

Divide both sides by

$y = \frac{\log_{e} (36)}{2}$

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Example Question #152 : Algebra

$10 \times 3^{\frac{3t}{4}} = 200$

Possible Answers:

$\frac{3}{4} \times \frac{\\\log {20}}{\log{3}} = t$

$\frac{4}{3} \times \frac{\\\\log{3}}{\log{20}} = t$

$\frac{3}{4} \times \frac{\\\\log{3}}{\log{20}}$

$\frac{4}{3} \times \frac{\\\log {20}}{\log{3}} = t$

Correct answer:

$\frac{4}{3} \times \frac{\\\log {20}}{\log{3}} = t$

Explanation:

$10 \times 3^{\frac{3t}{4}} = 200$

Isolate the variable by dividing both sides of the equation by 10.

$3^{\frac{3t}{4}} = 20$

Write in logarithm form.

$\log_{3}= (20)\frac{3^{t}}{4}$

$\frac{4}{3}\log_{3} (20) = t$

Because the solution is in base-3 log, it can be changed to base -10 by using:

$\log_{b} (a) = \frac{\log_{x}(a)}{\log_{x}(b)}$

$\frac{4}{3}\log_{3} (20) = t$

$\frac{4}{3} \times \frac{\\\log {20}}{\log{3}} = t$

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Example Question #153 : Algebra

Solve for x: $2^{x+1}=128$

Possible Answers:

x=10

x=5

x=7

x=6

Correct answer:

x=6

Explanation:

Step 1: Rewrite the right side of the equation into a power of 2.

$128=2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2=2^7$

$2^{x+1}=2^7$

Step 2: We have the same base, so we can equate the exponents.

x+1=7

Step 3: Solve for x. We will subtract 1 from both sides to isolate x.

x+1-1=7-1
$\rightarrow x=6$

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Example Question #154 : Algebra

Solve for :

$2^{x^2-3x}=4^{5}$

Possible Answers:

x=-5

x=-5, x=2

x=-2

x=5, x=-2

Correct answer:

x=5, x=-2

Explanation:

Step 1: Rewrite 4^5 as 2^n .

$4^5 \equiv 2^{10}$

n=10

Step 2: Re-write the equation:

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

Step 3: By laws of exponents, if the bases are the same, we can equate the exponents...

We will get x^2-3x=10

Step 4: Move 10 over and begin factoring:

x^2-3x-10=0
(x-5)(x+2)=0
x=5, x=-2

Step 5: x=-2 is a correct answer... we can plug it in and see:

$2^{(-2)^2-3(-2)}=2^{4--6}=2^{10}$

Step 6: x=5 is the other correct answer...

$2^{(5)^2-3(5)}=2^{25-15}=2^{10}$

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Example Question #155 : Algebra

Solve: 2^x=4^3

Possible Answers:

x=6

x=9

x=2

x=4

Correct answer:

x=6

Explanation:

Step 1: Rewrite the right hand side of the equation as a power of 2.

$4^3\equiv 2^6$ . To get this, divide the base by 2 and multiply that 2 to the exponent...

Step 2: Equate the left and right side together

2^x=2^6

We have the same base, so we equate the exponents together..

x=6 ...

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Example Question #156 : Algebra

Solve for :

2^x=8^3

Possible Answers:

x=10

x=8

x=9

$x=\frac {1}{9}$

Correct answer:

x=9

Explanation:

Step 1: Write 8^3 as 2^n ...

$8\cdot8\cdot8=(2\cdot 2\cdot 2)(2\cdot 2\cdot 2)(2\cdot 2\cdot 2)=2^9$

Step 2: Rewrite 8^3 as 2^9 in the original equation..

2^n=2^9

Step 3: By a rule of exponents, I can set the exponents equal if the bases of both exponents are the same...

So, n=9

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Example Question #157 : Algebra

Solve for :

$2^{x+1}=8^4$

Possible Answers:

x=-7

x=4

x=11

x=-11

Correct answer:

x=11

Explanation:

Step 1: Rewrite the right side as a power of :

$8^4=8\cdot8\cdot8\cdot8$

8=2^3

$8^4=2^3\cdot2^3\cdot2^3\cdot2^3$

$8^4=2^{3+3+3+3}=2^{3\cdot 4}=2^{12}$

Step 2: Rewrite the original equation:

$2^{x+1}=2^{12}$

Step 3: Since the bases are equal, I can set the exponents equal.

So, $x+1=12\implies x=11$

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Example Question #158 : Algebra

Solve for :

$2^{x+3}=8^4$

Possible Answers:

Correct answer:

Explanation:

Rewrite the right hand side such that it has the same base as the expression on the right hand side.

$8^4=\big(2^3\big)^{4}$
Apply the rule of stacked exponents. We multiply the exponents together and keep the same base:

$\large \big(2^3\big)^4=2^{3\cdot4}=2^{12}$

Now that we have rewrote the right hand side in the same way as the left, we can equate them:

$\large 2^{x+3}=2^{12}$

Now that we have the same bases, we can equal the exponents and solve for x...

$\large x+3=12 \implies x=9$

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Example Question #159 : Algebra

Find the value that makes the statement $(36)^{x+2}=6$ true.

Possible Answers:

$\frac {1}{2}$

$\frac {3}{2}$

$-\frac {3}{2}$

Correct answer:

$-\frac {3}{2}$

Explanation:

Step 1: Re-write the left side so we have the same base as the right side...

$(36)^{x+2}=6\implies (6^2)^{x+2}=6^1$

Step 2: Multiply the stacked exponents on the left hand side...

We will apply the rule: $(a^b)^c=a^{b\cdot c}$

So, $(6^2)^{x+2}=6^{2(x+2)}=6^{2x+4}$

Step 3: We can now set the exponents equal to each other, since we have the same base.

2x+4=1

2x=1-4

2x=-3

$\frac {{\color{Blue} 2}x}{{\color{Blue} 2}}=-\frac {{\color{Red} 3}}{{\color{Blue} 2}}$

$x=-\frac {3}{2}$

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Example Question #160 : Algebra

Find one possible value of , given the following equation:

$343=7^{15t-12}$

Possible Answers:

Cannot be determined from the information given.

t=1

t=5

t=-3

t=0

Correct answer:

t=1

Explanation:

We begin with the following:

$343=7^{15t-12}$

This can be rewritten as

$7^3=7^{15t-12}$

Recall that if you have two exponents with equal bases, you can simply set the exponents equal to eachother. Do so to get the following:

3=15t-12

Solve this to get t.

15=15t

t=1

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GRE Subject Test: Math : Algebra

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #151 : Algebra

Example Question #152 : Algebra

Example Question #153 : Algebra

Example Question #154 : Algebra

Example Question #155 : Algebra

Example Question #156 : Algebra

Example Question #157 : Algebra

Example Question #158 : Algebra

Example Question #159 : Algebra

Example Question #160 : Algebra

All GRE Subject Test: Math Resources

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