How to find an exponent from a rational number

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

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1

Com_exp_1

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

I, IV, III, II

0

II, III, I, IV

0

I, III, II, IV

CORRECT

IV, III, II, I

0

I, IV, II, III

0

Explanation

Com_exp_2

Com_exp_3

2

Solve for .

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

$-5\ or\ 2$

0

$5\ or\ -2$

0

0

0

CORRECT

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:

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

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

CORRECT

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

0

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

0

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

0

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

0

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

0

27

CORRECT

36

0

40

0

125

0

Explanation

The answer is 33 = 27

5

Solve for .

$2^{x}= 64$

CORRECT

0

0

0

$x=64^{2}$

0

Explanation

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

Hence

6

Solve for :

$\sqrt{x} -1= 4$

CORRECT

0

0

0

0

Explanation

From the equation one can see that

$\sqrt{x} = 5$

Hence must be equal to 25.

7

Solve for .

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

CORRECT

0

0

0

0

Explanation

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

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

8

Evaluate:

$\log 0.1=$

CORRECT

0

0

$\frac{1}{10}$

0

0

Explanation

$0.1= 10^{-1}$

$\log 0.1=-1$

9

Solve for .

$\log_{2}x=4$

CORRECT

0

0

0

0

Explanation

$x= 2^4{}= 16$

10

$\log 3=a$

and

$\log 5=b$

Find $\log 15$

CORRECT

0

0

$a^{2}$

0

$b^{2}$

0

Explanation

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

Hence the correct answer is .

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