Exponentials and Logs Test Review

Solving Exponentials

100

evaluate: 2⁴=x

x=16

200

evaluate: 3^x=81

x=4

300

Solve for x: 9^(x+1)=3^(x+3)

x=1

400

Evaluate: 3^(x+1)+4=8

x=log_3(4)-1

500

Evaluate: 4e^(3x)=1

x=log_e(1/3)/3

Solving Logarithms

100

Evaluate Log₄64=x

x=3

200

Solve for x:

Log₇(2-x) = log₇5x

x=1/3

300

Solve for x: ln 3x=6

x=e^6/3 

400

Solve for x: 2log₄8x=6

x=8

500

Solve for x:

log₂x + log₂(x+2)=3

x=-3

Graphing

100

Is the following function growth or decay? And what is the y-intercept in (x,y) form?  y=-3(1/2)^x   

Decay and (0,-3) is the y-intercept

200

Is the following function growth or decay? And what is the y-intercept in (x,y) form?

y=1/4(4/3)^x

Growth and (0, .25)

300

Sketch the graph of the equation: f(x) = e^(x+3)-1

What is the equation of the asymptote?  

y=-1

400

Sketch the graph of the equation: y=ln(x-4)+2

What is the domain AND range of the graph?

Domain 4 , oo

Range -oo,oo

500

Sketch the graph of the equation: y=log₅x-3

What is the end behavior of the graph?

x->oo y->oo

x->0 y->-oo

Log Properties

100

Rewrite the function in exponential form:

log₉81=2

9²=81

200

Rewrite the function in logarithmic form:

8²=64

log₈64=2

300

Expand the following logarithm:

log₃3x⁴

log₃3 + 4log₃x

400

Condense the logarithm: 2log4 - log2

log8

500

Condense the following logarithm:

Log₅4 + 2log₅x - 4log₅b

log_5(4x^2/b^4)

Word Problems

100

Suppose you invest $3300 into a savings account with a 3.5% interest rate. What is the rate value that you would use in the formula

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

3.5 

div 100= .035

200

Suppose you invest $3300 into a savings account with a 3.5% interest rate. How much money would be in the account after 6 years if the interest is compounded monthly?

$4,069.89 

300

 Suppose you invest $3300 into a savings account with a 3.5% interest rate. How much money would be in the account after 6 years if the interest is compounded continuously?

$4,071.14

400

Suppose you purchase a house for $275,000 in 2010.  The value of the house is supposed to increase by  8% each year, so when will the house be worth $500,000? Round to the nearest year.

Using the formula: 

A=P(1+-r)^t

8 years

500

The difference in magnitudes of two earthquakes is defined by

M_1-M_2=log (I_1/I_2) where I_1/I_2

is the ratio of the intensities of the earthquakes.  Solve this equation for I₁ , the intensity of the first earthquake.

I₂ x 10^(M₁-^M₂⁾=I₁