Exponential Ratios and Rational Numbers

Help Questions

PSAT Math › Exponential Ratios and Rational Numbers

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

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

3

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 .

4

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 .

5

For some positive integer , if , what is the value of ?

Explanation

If , then must equal 3 (Note that cannot be -3 because you need it to be positive.

Now, plug into the new equation :

6

For some positive integer , if , what is the value of ?

Explanation

If , then must equal 3 (Note that cannot be -3 because you need it to be positive.

Now, plug into the new equation :

7

$Simplify: \frac{\sqrt[3]{81}}{\sqrt[3]{3}}$

$\sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \frac{3}{1}= 3$

$\frac{81}{3}= 27$

$\sqrt[3]{81\star 3}= \sqrt[3]{243} = 6.24$

$\frac{\sqrt[3]{9\star 9}}{\sqrt[3]{9}}= \sqrt[3]{9}$

Explanation

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

8

$Simplify: \frac{\sqrt[3]{81}}{\sqrt[3]{3}}$

$\sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \frac{3}{1}= 3$

$\frac{81}{3}= 27$

$\sqrt[3]{81\star 3}= \sqrt[3]{243} = 6.24$

$\frac{\sqrt[3]{9\star 9}}{\sqrt[3]{9}}= \sqrt[3]{9}$

Explanation

$\frac{\sqrt[3]{81}}{\sqrt[3]{3}} = \sqrt[3]{\frac{81}{3}}= \sqrt[3]{27}= 3$

9

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

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

10

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

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

Page 1 of 4

Return to subject