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PSAT Math : Exponents

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Example Question #267 : Exponents

Simplify:

$log\left (\frac{x}{y^{2}} \right )$

Possible Answers:

$logx+logy^{2}$

logx-2logy

2logy-logx

$\left ( logx \right )\left ( logy^{2} \right )$

$logx-logy^{2}$

Correct answer:

logx-2logy

Explanation:

$log\left ( \frac{x}{y^{2}} \right )=logx-logy^{2}$

Now $logy^{2} = 2logy$

Hence the correct answer is logx - 2logy

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Example Question #268 : Exponents

Solve for .

$\ln x=\ln (x-1)-\ln (x+3)$

Possible Answers:

$no\ solution$

Correct answer:

Explanation:

If we combine into a single logarithmic function we get:

$\ln x=\ln \frac{x-1}{x+3}$

$x = \frac{x-1}{x+3}$

Solving for we get x=-1 .

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Example Question #269 : Exponents

If is the complex number such that i^2=-1 , evaluate the following expression:

$i^{25}-i^{23}+i^{21}-i^{19}+i^{17}-i^{15}.\ .\ .+i$

Possible Answers:

13i

-25i

12i

Correct answer:

13i

Explanation:

The powers of i form a sequence that repeats every four terms.

i¹= i

i² = -1

i³ = -i

i⁴ = 1

i⁵ = i

Thus:

i²⁵ = i

i²³ = -i

i²¹ = i

i¹⁹= -i

Now we can evalulate the expression.

i²⁵ - i²³+ i²¹- i¹⁹ + i¹⁷..... + i

= i + (-1)(-i) + i + (-1)(i) ..... + i

= i + i + i + i + ..... + i

Each term reduces to +i. Since there are 13 terms in the expression, the final result is 13i.

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Example Question #1 : How To Use Scientific Notation

Express 0.000000076 in scientific notation.

Possible Answers:

$7 6 \times 10^{-9}$

$7.6 \times 10^{-9}$

$0.76\times 10^{-8}$

$7 6 \times 10^{-8}$

$7.6 \times 10^{-8}$

Correct answer:

$7.6 \times 10^{-8}$

Explanation:

Write the number:

$0.000\; 000\; 076$

Counting the number of places, move the decimal point to the right until it is after the first nonzero digit:

$0 \; 000\; 000\; 07.6$

The resulting number is 7.6; the number of places the decimal point moved to the right was 8. In scientific notation, this number is $7.6 \times 10^{-8}$ .

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Example Question #1 : How To Use Scientific Notation

Express the square of $7 \times 10^{15}$ in scientific notation.

Possible Answers:

$4.9 \times 10^{16}$

$4.9 \times 10^{31}$

$49 \times 10^{30}$

$49 \times 10^{225}$

$4.9 \times 10^{226}$

Correct answer:

$4.9 \times 10^{31}$

Explanation:

Take advantage of the exponent rules.

$\left (7 \times 10^{15} \right )^{2}$

$= 7^{2} \times \left ( 10^{15} \right )^{2}$

$= 49 \times 10^{15 \times 2}$

$= 49 \times 10^{30}$

$= 4.9 \times 10^{1} \times 10^{30}$

$= 4.9 \times 10^{1+30}$

$= 4.9 \times 10^{31}$

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Example Question #1 : How To Use Scientific Notation

The number 0.0000279 is equivalent to which of the following?

Possible Answers:

$2.79\cdot 10^{5}$

$2.79\cdot 10^{4}$

$2.79\cdot 10^{-6}$

$2.79\cdot 10^{-4}$

$2.79\cdot 10^{-5}$

Correct answer:

$2.79\cdot 10^{-5}$

Explanation:

Each of the answers to this question are in scientific notation. To determine the exponent on the 10, see how many places you need to move the decimal over to get from your original number to 2.79.

Scientific_notation

Because the decimal place moves 5 places, the exponent will be 5, and because the decimal moves to the RIGHT, the exponent is going to be negative.

So the answer to the quesiton is $2.79\cdot 10^{-5}$

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Example Question #61 : Exponential Operations

Put the following value in scientific notation:

19540000

Possible Answers:

$1.954 \times 10^{6}$

$1.954 \times 10^{7}$

$19.54 \times 10^{7}$

$1954 \times 10^{4}$

Correct answer:

$1.954 \times 10^{7}$

Explanation:

Our first value for scientific notation should be between and . We then multiply this value by raised to a power equal to the number of spaces our decimal has moved to the left.

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PSAT Math : Exponents

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #267 : Exponents

Example Question #268 : Exponents

Example Question #269 : Exponents

Example Question #1 : How To Use Scientific Notation

Example Question #1 : How To Use Scientific Notation

Example Question #1 : How To Use Scientific Notation

Example Question #61 : Exponential Operations

All PSAT Math Resources

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