Unit 12 – Day 2 Name: Date: Integrated Math 4G: NOTES Logs and Exponents – Solving Exponential Equations using Logarithms Over the next few days, we will be talking about logarithms (logs). This is something a lot of you have probably covered in Algebra 2. We will continue to work with them and (hopefully) understand them better. For today, the only thing you really need to know is how do take a logarithm on a calculator. In the next few days, we will work with logs without using a calculator.

Calculators like these can only take a log to “base 10”:

SOME calculators like these can take a log to any base

(depending on how new it is).

Calculators like these can take a log to any base.

TI-30 TI-83

TI-84

TI-84 COLOR

Steps to take a “log base 10” Steps to take a “log base 𝑏” 1)

Press the “LOG” button. When there is no base for the log, it is understood to be 10 – so we do not have to type 10 in.

1)

Press the “ALPHA” button, followed by the “WINDOW” button, followed by choosing the “logBASE(” choice on the screen. It will most likely be the 5th choice.

2)

Type in a number and press “ENTER”.

2)

Type your base and number.

3)

Press “ENTER”.

Unit 12 – Day 2 Calculate the following logarithms using a calculator. Round to the nearest hundredth if necessary. Ex 1) log101000 = Ex 2) log1062 = Ex 3) log636 = Ex 4) log548 = Solving Exponential Equations with an Exponent only on One Side:

Rule: 𝑏𝑥 = 𝑐 ⟹ log𝑏𝑏𝑥 = log𝑏𝑐 ⟹ 𝑥 = log𝑏𝑐

Find the value of 𝑥 using the rule above. Round to the nearest hundredth if necessary. Ex 5) 4𝑥 = 64 Steps: 1) Take the log to your base of both sides. 2) The exponent drops down and the log and

original base cancel. 3) Solve for 𝑥 (get 𝑥 by itself). Ex 6) 6−𝑥+3 = 36 Ex 7) 84𝑥+3 = 77 Ex 8) 22𝑥+3 = 64 Ex 9) 108𝑥+2 = 34

Unit 12 – Day 2 Name: Date: Integrated Math 4G: HMWK Logs and Exponents – Solving Exponential Equations using Logarithms (#1-11) Solve the following exponential equations using logarithms. Round all answers to the nearest hundredth. 1) 3𝑥 = 243 2) 5𝑥 = 3125

3) 2𝑥 = 164

4)

5𝑥 = 12.5

5) 32𝑥+1 = 47 6) 45−𝑥 = 122

Unit 12 – Day 2 7) 7𝑥−3 = 451 8) 82𝑥+1 = 72

9) 6𝑥+5 = 72 10) 122𝑥 = 189

11) 93𝑥−4 = 173