Exponents, Roots and Logarithms

Exponents, Roots and Logarithms

Mr. G. Green

Multiple Choice

10³ = 1000

10³ = ?

"What is 10 cubed?":

• 10³ = 1000

• ∛1000 = 10

• log₁₀(1000) = 3

Multiple Choice

10³ = 1000

?³ = 1000

"What is the cube root of 1000?":

• 10³ = 1000

• ∛1000 = 10

• log₁₀(1000) = 3

Multiple Choice

10³ = 1000

10^? = 1000

"What is log base 10 of 1000?":

• 10³ = 1000

• ∛1000 = 10

• log₁₀(1000) = 3

Exponents

The exponent of a number says how many times to use the number in a multiplication.

In 8² the "2" says to use 8 twice in a multiplication, so 8² = 8 × 8 = 64

2^4 is the same as 2⁴

Negative Exponents

• Negative? What could be the opposite of multiplying? Dividing!

• So we divide by the number each time, which is the same as multiplying by 1/number

Multiple Choice

What is the value of 6³ ?

• 18

• 216

• 729

• 1296

Multiple Choice

What is the value of 2^-4?

• -8

• 0.125

• 0.0625

• 16

Multiple Choice

What is the value of (-3)⁵?

• -243

• -125

• 125

• 243

Multiple Choice

What is the value of (-5)-3?

•  $-\frac{1}{243}$  

•  $\frac{1}{243}$  

•  $\frac{1}{125}$  

•  $-\frac{1}{125}$  

Logarithms Can Have Decimals

How can we do half a multiply?

 

Well, half a multiply is something we need to do twice to make a whole multiply.

 

And that is square root!

Multiplying by a square root is like doing half a multiply.

• So let us try that:

• Example: log10(300)

Fill in the Blanks

What is log10(640) ?

[give correct to 3 decimal places]

Multiple Choice

What is the value of log_e(5) ?

(Use your calculator)

log_e(5) is also called ln(5), the natural logarithm of 5

• 0.621

• 0.699

• 1.431

• 1.609

Multiple Choice

What is the value of log₁₀(12) ?

(Use your calculator)

• 0.402

• 0.927

• 1.079

• 2.485

Multiple Choice

What is the value of log_e(3³) ?

(Use your calculator)

• 0.109

• 1.326

• 1.431

• 3.296

Multiple Choice

What is the value of log_e(42) − log_e(7) ?

(Use your calculator)

• 3.555

• 1.792

• 1.544

• 0.778

Multiple Choice

What is the value of log₁₀(20) + log₁₀(0.25) ?

(Use your calculator)

• 0.699

• 1.306

• 1.609

• 3.008

What is the value of log₁₀(20) + log₁₀(0.25) ?

log₁₀(20) + log₁₀(0.25) = log₁₀(20 × 0.25) = log₁₀(5)

log₁₀(5) is called log(5) on your calculator.

Use the log button on your calculator.

⇒ log₁₀(5)= log(5) = 0.699 correct to three decimal places

End of Class

Thank you for completing this lesson