Exponential and Logarithmic Functions - Properties of Exponents

SOURCE:COMPETITION
Number of Problems: 8. : (Book)

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What is the value of $frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}} ?$

$extbf{(A)} -1 qquad extbf{(B)} 1 qquad extbf{(C)} frac{5}{3} qquad extbf{(D)} 2013 qquad extbf{(E)} 2^{4024}$

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3.

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Find the value of $x$ that satisfies the equation $25^{-2} = frac{5^{48/x}}{5^{26/x} cdot 25^{17/x}}.$

$extbf{(A) } 2 qquad extbf{(B) } 3 qquad extbf{(C) } 5 qquad extbf{(D) } 6 qquad extbf{(E) } 9$

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4.

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Suppose that $4^a = 5$ , $5^b = 6$ , $6^c = 7$ , and $7^d = 8$ . What is $a cdot bcdot c cdot d$ ?

$mathrm{(A)} 1 qquad mathrm{(B)} frac{3}{2} qquad mathrm{(C)} 2 qquad mathrm{(D)} frac{5}{2} qquad mathrm{(E)} 3$

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6.

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What non-zero real value for $x$ satisfies $(7x)^{14}=(14x)^7$ ?

$mathrm{(A) } frac17qquad mathrm{(B) } frac27qquad mathrm{(C) } 1qquad mathrm{(D) } 7qquad mathrm{(E) } 1...$

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7.

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Real numbers $a$ and $b$ satisfy the equations $3^{a} = 81^{b + 2}$ and $125^{b} = 5^{a - 3}$ . What is $ab$ ?

$ext{(A)} -60 qquad ext{(B)} -17 qquad ext{(C)} 9 qquad ext{(D)} 12 qquad ext{(E)} 60$

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8.