Warm Up Solve for x: 𝟑+𝟐∙ 𝟒 𝒙 =𝟐𝟓 𝒍𝒐𝒈 𝟔 𝟑𝒙−𝟐 +𝟏=𝟏 I can solve exponential equations using properties of logarithms Warm Up Solve for x: 𝟑+𝟐∙ 𝟒 𝒙 =𝟐𝟓 𝒍𝒐𝒈 𝟔 𝟑𝒙−𝟐 +𝟏=𝟏 Condense or Expand using log properties 𝒍𝒐𝒈 𝟒 𝒙−𝟏 − 𝒍𝒐𝒈 𝟒 𝒙 𝒍𝒐𝒈 𝟐 𝟓 𝒙 𝟑 𝒚 𝟐

Warm Up Solve for x: 𝟑+𝟐∙ 𝟒 𝒙 =𝟐𝟓

Warm Up Solve for x: 𝒍𝒐𝒈 𝟔 𝟑𝒙−𝟐 +𝟏=𝟏

Warm Up Condense or Expand using log properties 𝒍𝒐𝒈 𝟒 𝒙−𝟏 − 𝒍𝒐𝒈 𝟒 𝒙 𝒍𝒐𝒈 𝟒 𝒙−𝟏 − 𝒍𝒐𝒈 𝟒 𝒙 𝒍𝒐𝒈 𝟐 𝟓 𝒙 𝟑 𝒚 𝟐

Homework Questions

Natural Log What is the approximate value of 𝜋? What is the approximate value of e? In math, e is known as Euler’s number. It has an approximate value of 2.718. 𝑙𝑜𝑔 𝑒 is known as the “natural log” which is represented 𝑙𝑛

Natural Log Examples: 𝑙𝑛10= ln 𝑥 =4 𝑒 2𝑥−1 =12

𝑥=28 𝑥=9 𝑥=4 𝑥=45.25 𝑥=2 Practice 𝑙𝑜𝑔 5 5𝑥−15 =3 2 𝑙𝑜𝑔 3 𝑥=4 Solve each equation for x. Note: you may need to condense first! 𝑙𝑜𝑔 5 5𝑥−15 =3 2 𝑙𝑜𝑔 3 𝑥=4 𝑙𝑜𝑔 2 4𝑥−12 −3=−1 𝑙𝑜𝑔 8 𝑥+ 𝑙𝑜𝑔 8 2𝑥 =4 𝑙𝑜𝑔 7 4𝑥+90 − 𝑙𝑜𝑔 7 𝑥=2 𝑥=28 𝑥=9 𝑥=4 𝑥=45.25 𝑥=2

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Solve for x 𝑥 2 −5𝑥−6=0

Evaluate the function: If 𝑔 𝑥 = 𝑥 3 +5 𝑥 2 , find 𝑔(4𝑥)

Solve for x 6 7𝑥 2 +1 = 492 5

Solve for x. Round to the nearest thousandth. 20 𝑥 −8=−1.9

Find the inverse function: 𝑓 𝑥 =3+ 𝑥 3

Solve for x −1−26𝑥 −4=1

Solve for x 1 3𝑥 = 3 𝑥 + 1 3

Solve for x − 𝑥−1 +6𝑥=−11+3𝑥

Solve for x 2 𝑥 2 3 +1=9

Solve the system 𝑦=5𝑥+1 2𝑥−4𝑦=−22

Solve for x − 𝑥 2 =−10𝑥−4 𝑥 2 +8

Solve the system −𝑥−2𝑦=0 𝑦=−2

Evaluate the function: If 𝑓 𝑥 = 𝑥 2 +2𝑥, find 𝑓(3+𝑥)

Solve for x. Round to the nearest thousandth. 10 7𝑥 +1=5

Find the inverse function: 𝑓 𝑥 = −6+ 3 4𝑥 2

Homework Textbook 7-120, 7-132, 7-134, 7-136, and 7-140