Exponential and Logarithmic Transformation

Convert the exponential equation `e^5 = 148.413` to logarithmic form, using the natural logarithm.

• ln(148.413) = 5

• ln(5) = 148.413

• ln(e) = 5/148.413

• ln(148.413) = e^5

Convert the exponential equation `9^1.5 = 27` to logarithmic form.

• log9(27) = 1.5

• log1.5(27) = 9

• log27(9) = 1.5

• log27(1.5) = 9

Convert the logarithmic equation `log(1/100) = -2` to exponential form.

• 10^(-2) = 1/100

• 10^(1/100) = -2

• (1/100)^10 = -2

• (1/100)^(-2) = 10

Convert the exponential equation `6^(-1) = 1/6` to logarithmic form.

• log6(1/6) = -1

• log(-1)(1/6) = 6

• log(1/6)(6) = -1

• log(-1)(6) = 1/6

Convert the logarithmic equation `log2(32) = 5` to exponential form.

• 2^5 = 32

• 2^32 = 5

• 32^2 = 5

• 32^5 = 2

Convert the logarithmic equation `log5(1/125) = -3` to exponential form.

• 5^(-3) = 1/125

• 5^(1/125) = -3

• (1/125)^5 = -3

• (1/125)^(-3) = 5

Convert the logarithmic equation `log7(1) = 0` to exponential form.

• 7^0 = 1

• 7^1 = 0

• 1^7 = 0

• 0^7 = 1

Convert the logarithmic equation `ln(e^3) = 3` to exponential form.

• e^3 = 3

• e^3 = e

• 3^e = e

• e^3 = e^3

Match the graph with its equation

• y = log₅ (x + 1) + 1 

• y = log₅ (x - 1) + 1 

• y = log₅ (x²) + 1 

• y = log₅ (x)-1

Describe the transformations of the exponential function shown.

• Stretch by a factor of 7, shift left 4, and shift down 7.

• Stretch by a factor of 7, shift right 4, and shift down 7.

• Shrink by a factor of 7, shift left 4, and shift down 7.

• Stretch by a factor of 7, shift left 4, and shift up 7.