How to find an exponent from a rational number

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

Questions 1 - 10

1

Com_exp_1

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

I, IV, III, II

II, III, I, IV

I, III, II, IV

IV, III, II, I

I, IV, II, III

Explanation

Com_exp_2

Com_exp_3

2

Solve for .

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

$-5\ or\ 2$

$5\ or\ -2$

Explanation

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 .

3

Simplify:

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

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

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

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

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

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

Explanation

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

4

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?

12

27

36

40

125

Explanation

The answer is 33 = 27

5

Solve for .

$2^{x}= 64$

$x=64^{2}$

Explanation

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

Hence

6

Solve for .

$\log_{2}x=4$

Explanation

$x= 2^4{}= 16$

7

Evaluate:

$\log 0.1=$

$\frac{1}{10}$

Explanation

$0.1= 10^{-1}$

$\log 0.1=-1$

8

Solve for :

$\sqrt{x} -1= 4$

Explanation

From the equation one can see that

$\sqrt{x} = 5$

Hence must be equal to 25.

9

Solve for .

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

Explanation

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

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

10

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

$a^{2}$

$b^{2}$

Explanation

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

Hence the correct answer is .

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