12.5/12.7 Solving Exponential and

Logarithms Brett Solberg AHS ’11-’12

1) Expand the Logarithm

2) Simplify the expression to one logarithm

Have your HW out for stamps and questions You need a scientific calculator!

Warm-up

Courtney, Josi, Rachel, Arthur

Quiz Retakes

12.5 Calculating Logarithms and Antilogarithms

12.7 Solving Exponential and Logarithmic Equations Solving Interest and loudness formulas

Today’s Agenda

A logarithm with base 10 is a common logarithm.

We can easily calculate common logs using a calculator.

Common Logarithms

log 7.09

log 4.00

log 9.99

Common Logarithms

Common Logarithm 7 = x 10x = 7

Antilogarithm 107 = x antilog4.3425

Antilogarithm

antilog 3.0098 = antilog – 3.0067 = antilog -6.7628 = antilog 4.8069 = antilog(6.6284-10) =

Antilogarithm

Solve for x

= 4

x2 + 2 = 11

Square cancels a square root Square root cancels square

Review

You get variables out of equations using logs

5x = 7 35x – 2 = 8

Solving Exponential Equations

35x – 2 = 27 4x = 6 42x – 3 = 64

Solving Exponential Equations

we eliminate logs by raising both sides by its base

4

Solving Logarithmic Equations

log(x – 1) + log(x + 1) = 1

logx + log(x + 3) = 1

Solving Logarithmic Equations

A = P(1 + r)t

Annual Compound Interest

Resulting Amount

PrincipleAmount

rate(decimal

)

time(years)

Suppose $5,000 was invested at 14%, compounded annually, and it yielded $18,540. For how long was it invested?

InterestA = P(1 + r)t

Suppose $1,000 is invested at 8%, compounded yearly. How long will it take for the investment to grow to $2,000?

InterestA = P(1 + r)t

𝐿=10 𝑙𝑜𝑔 𝐼𝐼0

Loudness

Loudness(bells)

minimal intensit

y

Intensity

Find the loudness in decibels of the sound in a library for which the intensity is 2510 times

Loudness

𝐿=10 𝑙𝑜𝑔 𝐼𝐼0

Find the loudness in decibels of conversational speech for which the intensity is 106 times

Loudness

𝐿=10 𝑙𝑜𝑔 𝐼𝐼0

12.7 pg 547 1 – 27 all, skip 22 and 23

Homework