2-4: Exponential and Logarithmic Equations

example 1

100

4^x+7=8^x+3

x= 5

200

12^3x+11=144^2x+7

x= -3

300

(9/16)^3x-2=(3/4)^5x+4

x= 8

400

(5/6)^4x=(36/25)^9-x

x= -9

500

The number of people P in millions using two different search engines to surf the Internet t weeks after the creation of the search engine can be modeled by P₁(t)=1.5^t+4 and P₂(t)=2.25^t-3.5 , respectively. 

During which week did the same number of people use each search engine?

During week 11

example 2

100

ln a=4

a = 54.60

200

log₂ m⁴=32

m=256

300

14+20ln7x=54

x=1.06

400

100+500log₄ g=1100

g=16

500

-18log₀ j=-126

j=0

example 3

100

log₆(x²+5)=log₆41

x=6

200

log₉(x⁴-3)=log₉13

x=2

300

log₇6x=log₇9+log₇(x-4)

x=12

400

log₅x=log₅(x+6)-log₅4

x=2

500

log₁₁3x=log₁₁(x+5)-log₁₁2

x=1