Transformations and Logarithmic

Rewrite log₂8 = 3 in exponential form.

• 2⁸ = 3

• 2³ = 8

• 3² = 8

• 8³ = 2

Write 2³= 8 in logarithmic form.

• log₂ 8 = 3

• log₂ 3 = 8

• log₃ 8 = 2

• log₃ 2 = 8

Write log₃ 81 = 4 in exponential form.

• 81⁴=3

• 81³=4

• 4³=81

• 3⁴=81

Write 10⁴= 10000 in logarithmic form.

• log₁₀ 4 = 10000

• log₁₀₀₀₀ 4 = 10

• log₁₀ 10000 = 4

• log₄ 10000 = 10

Evaluate: log₆₄4 = x

• x = 3

• x = -3

• x = ⅓

• x = -⅓

y = log_bx is equivalent to the exponential form _____, x>0, b>0, b≠1.

• b^x=y

• b^y=x

• y^x=b

• x^y=b

The function f(x) = log_bx is the ___________ function with base _________.

• exponential, b

• exponential, x

• logarithmic, b

• logarithmic, x

• Translated 2 units up

• Reflected over the y-axis

• Vertical dilation by a factor of 2 with respect to the x-axis

• Translated 1 unit right

Determine the transformations of the logarithmic functions from their parent function. Check all that apply.

• Vertical dilation by a factor of 1/2

• Horizontal dilation by a factor of 2

• Translated 3 units right

• Translated 1 unit down

• Reflected over the x-axis

• Dilated horizontally by a factor of 3

• Reflected over the y-axis

• Translated 2 units left and 1 unit down