Exponential and Logarithmic Equations

Exponential Functions

100

Write the exponential form:

Log₂8=3

2³=8

200

Write the exponential growth formula.

f(x)=a(1+r)^x

300

Find n.

Log₂1/128 =n 

2ⁿ=1/128

2ⁿ=2^-7

n=-7

400

solve for x.

8^x-1=2^x+9

(2³)^x-1=2^x+9

3x-3=x+9

2x-3=9

2x=12

x=6

500

Solve for x

4^2x=16^3x-1

4^2x =(4²)^3x-1

2x=6x-2

-4x=-2

x=2/4

x=1/2

Logarithmic Functions

100

Write the logarithmic form:

36²=1296

Log₃₆(1296)=2

200

Evaluate the logarithm:

log₈(1/2)

=-1/3

300

Solve:

log₈(128)=n

n= 7/3

400

Write the multiplication formula of log 

log_a(x)(y)=log_ax+log_ay

500

Solve for x.

log₄(x²-30)=log₄x

x²-30=x

x²-x-30

(x-6)(x+5)

x=6

x=-5, extraneous

Exponential Functions

100

Write the exponential form:

log₅(1/125)=-3

5^-3=1/125

200

Write the compound interest per year formula.

A=P(1 +r/n)^nt

300

solve for x.

9^2x=1/27

(3²)^2x=1/3³

3^4x=3^-3

4x=-3

x=-3/4

400

You invest 19,000 at an annual rate of 5.5%. Find the balance after 11 years.

=1900(1 + 0.055/1)^(1)(11)

=1900(1.055)¹¹

=3423.98

500

Solve using one to one property.

5^2x * 5^3x+1= 1/625

5^{2x + 3x+ 1} = 1/5⁴

5^2x+3x+1=5^-4

5x+1=-4

5x=-5

x=-1

Logarithmic Functions

100

Write the the logarithmic form:

15³=3,375

Log₁₅(3,375)=15

200

Evaluate the logarithm:

log₆(216)

=3

300

Solve for x using the one to one property.

ln(x²-x)=ln 2

x=2

x=-1

400

solve for x

log₈x=4/3

8^4/3=x

cube sqrt 8⁴

2⁴=x

x=16

500

solve for x.

log₄x²=log₄(x+20)

x²=x+20

x²-x-20

(x+4)(x-5)

x=-4 x=5

Vocabulary

100

What is the logarithmic formula?

Log_b(a)=C <---> B^c= a

200

What is the regular notation of a natural log?

Log_e(x)

300

Write the one to one property

log_aX=log_aY

    X=Y

400

write the division property of log.

log_ax/y =log_ax-log_ay

500

Write the 2 properties of log.

-log_a1=0

-log_aa=1

-log_aa^x=x

- If log_ax=log_ay, then x=y