How to find an exponent from a rational number - PSAT Math

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Question

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?

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Answer

The answer is 33 = 27

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Question

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

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Answer

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Question

Solve for .

$2^{x}= 64$

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Answer

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

Hence

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Question

Simplify:

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

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Answer

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

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Question

Solve for :

$\sqrt{x} -1= 4$

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Answer

From the equation one can see that

$\sqrt{x} = 5$

Hence must be equal to 25.

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Question

Evaluate:

$\log 0.1=$

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Answer

$0.1= 10^{-1}$

$\log 0.1=-1$

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Question

Solve for .

$\log_{2}x=4$

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Answer

$x= 2^4{}= 16$

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Question

Solve for .

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

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Answer

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

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

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Question

Solve for .

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

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Answer

Use the rules of logarithms to combine terms.

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

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

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

By fatoring we get

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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Question

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

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Answer

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

Hence the correct answer is .

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Question

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?

Tap to reveal answer

Answer

The answer is 33 = 27

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Question

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

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Answer

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Question

Solve for .

$2^{x}= 64$

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Answer

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

Hence

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Question

Simplify:

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

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Answer

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

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Question

Solve for :

$\sqrt{x} -1= 4$

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Answer

From the equation one can see that

$\sqrt{x} = 5$

Hence must be equal to 25.

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Question

Evaluate:

$\log 0.1=$

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Answer

$0.1= 10^{-1}$

$\log 0.1=-1$

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Question

Solve for .

$\log_{2}x=4$

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Answer

$x= 2^4{}= 16$

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Question

Solve for .

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

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Answer

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

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

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Question

Solve for .

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

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Answer

Use the rules of logarithms to combine terms.

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

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

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

By fatoring we get

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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Question

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

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Answer

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

Hence the correct answer is .

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