Solving Exponential Equations with Logarithms: Logarithms

Solving Simple Equations

100

Solve for x. 4^x = 16

x=2

200

Solve for x. ln x - ln 2 = 0

x=2

300

Solve for x. (1/4)^x = 64

x=-3

400

Solve for x. e^x = 2

x = ln 2 (approximately 0.639)

500

Solve for x using inverse property. Log₅ x=1/2

5^(1/2) = x, approximately 2.236

Logarithms

100

Write 3³= 27 in logarithmic form.

What is Log₃27 = 3

200

Write log₈4 = 2/3 in exponential form.

What is 8^2/3=4

300

Evaluate 5^log₅²⁵

What is 25

400

Solve log_b64 = 3

What is b=4

500

Solve for y Log₄(log₂16) = y

What is y=1

Logs

100

Simplify the expression: log₂ 8. In other words what exponent will equal 8?

What is 3

200

Write the equation log₃ 729 = 6 in exponential form.

What is 3⁶=729 

300

Write the equation log 1000 = 3 in exponential form.

What is 10³=1000

400

What is the asymptote of the graph of f(x) = log(x - 1) ?

What is x=1 

500

What is the asymptote of the graph of f(x)= log(x + 2) -1 ?

 

What is x= -2 

Fill in the blank

100

To _______ an equation for x means to find all values of x. 

Solve

200

a^x = a^y, meaning _________.

x = y

300

log_x = log_y meaning __________.

x = y

400

Inverse property for Natural log:

 

e(ln)^X  = X     →     ln(e)^X = X

500

First step of Solving Exponential Equations

find the bases 

Exponential EQ's

100

Write the exponential equation 4⁵= 1,024 in logarithmic form.

What is log₄ 1,024 = 5 ?

200

Write the exponential equation 27^1/3 = 3 in logarithmic form.

What is log₂₇ 3 = 1/3 ?

300

Write the exponential equation (1/2)^-3=8 in logarithmic form.

What is log_1/2 8 = -3

400

Is the graph y= .7^x increasing or decreasing, and is it a function?

Decreasing and yes

500

Simplify ln e^3x

What is 3x?