What is this formula?

y=2^x

Which type of equation is this?

y=(1/10)^x

Which type of equation is this?

y=1/2(2)^x

What function is this?

y=ab^x

Solve:

3²ⁿ⁺¹=81

3²ⁿ⁺¹=3⁴

2n+1=4

2n=3

n=3/2

What is this property?

If b>1, then b^x>b^y if and only if x>y, and b^x<b^y if and only if x<y

State this equation's property

2^x=2⁸, then x=8

Property of Equality for Exponential Functions

Solve equation:

4^3p-1>1/256

4^3p-1>1/256

4^3p-1>4^-4

3p-1>-4

3p>-3

p>-1

3^n-2>27

3^n-2>3³

n-2>3

n>5

y=2(3)^x

growth or decay?

y=4*(1/3)^x

growth or decay?

Solve:

10³=1000

log₁₀1000

=3

Solve:

log₄n=5/2

n=4^5/2

n=(2²)^5/2

n=2⁵ or 32

Solving equations with two logarithms

log₅(p²-2)=log₅p

(cancel out log_x)

p²-2=p

p²-p-2

(p-2)(p+1)

p=-1,2

logarithmic to exponential inequality

log₂x>3

write in exponential form

log₅125=3

Evaluate

log₂16

2^y=16

2^y=2³

y=3

Solve

log₂1/8

2^y=1/8

2^y=2^-3

log_an=log_bn/log_ba

Solving exponential equations

3^x=11

log 3^x=log 11

x log 3=log 11

x=log 11/log 3

(use calculator to get rest of answer)

How to solve a logarithmic problem

log E=11.8+1.5M

log E=11.81.5(8.5)<--(Chilean Earthquake rating)

log E=24.5

10^{log E}=10^24.55

E=10^24.55

E≈3.55*10²⁴

Solve when log₃5≈1.4650, log₃20≈2.7268

log₃4=log₃20/5

log₃20-log₃5

2.7268-1.4650

=1.2618

Solve

3 log₅x-log₅4=log₅16

log₅x³-log₅4=log₅16

log₅(x³/4)=log₅16

x³/4=16

x³=64

x=4

Solve

log₄x+log₄(x-6)=2

log₄x(x-6)=2

x(x-6)=4²

x²-6x-16=0

(x-8)(x+2)=0

x=8,-2

Solve when log₃2≈.6309, log₃7≈1.7712

log₃18

log₃(2*3²)

.6309+1.7712²

What are common logarithms'?

Solve when log₄6≈1.2925

log₄36=log₄6²

2 log₄6

2(1.2925)

=2.585