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Fascinating Exponential Functions

LethargicLog Functions

EgotisticalProperties

Of Logs

OutrageousExponential

& Log Equations

AmazingExponential

& Log Models

Evaluatef(x) = 3.4x

When x = 5.6

What is 946.8516

Graph the functionf(x) = 2x-1

What is

Graph f(x) = 2ex – 2 + 4

What is

Solve the equation for xe2x – 1 = e4

WHAT IS 5/2?

Determine the balance for $2500 at a rate of 3% for 20 years

Compounded both monthly and continuously.

What is A $4535.05 when compounded monthlyWhat is $4555.30 compounded continuously?

Write the logarithmic equation in exponential form

log84 = 2/3

What is 82/3 = 4

Write the exponential equation in logarithmic form

e2 = 7.3890….

What is ln 7.3890….= 2

Use the properties of logs to simplify the expression

9log915

What is 15?

Find the domain, x-intercept, vertical or horizontal asymptotes of the logarithmic function and

sketch its graph.

f(x) = ln(3-x)

What is

Solve for x.

log (5x + 3) = log 12

What is x = 9/5?

Rewrite the logarithm as a ratio of common logsand natural logs

log 2.6 x

What is log x log 2.6

What is ln x ln 2.6

Evaluate the logarithm using the change of base formula

log151250

What is 2.6332?

Find the exact value of the logarithmic expression without using a calculator.

log3 81-0.2

What is-0.8?

Use the properties of logarithms to expand the expression as a sum, difference, and /or constant

multiple of logarithms.

Ln 4x3(x2 -4)

What is 3/4lnx +1/4[ln(x+2) + ln(x-2)]

Or

¼[3lnx + ln(x + 2) + ln (x – 2)]

Condense the expression to the logarithm of a single quantity.

½ [log (x + 1) + 2 log (x – 1)] + 6 log x

What is log [x6(x – 1)x + 1 ]

Solve for x

ln x = -7

What is e-7 ≈ .000912

Solve the exponential equation

6(23x – 1) – 7 = 9

What is 0.805

Solve for x

e0.125x – 8 = 0

What is 16.6355?

Solve the logarithmic equation algebraically.

log 4x – log (12 +x) = 2

What is 1225 + 125 75 ≈ 1146.5002

The number of endangered animal species in the US from 1990 to 2002 can be modeled by

Y = -119 + 164ln t , 10 ≤ t ≤ 22

Where t represent the year, with t = 10 corresponding to 1990. During which year did the number of

endangered animal species reach 357?

What is t = 18, which makes the year 1998.

How long will it take an initial investment of $600 at a rate of 4.5% to double if

compounded quarterly?

What is 1.2965 years?

Determine the rate at which $1000 will double compounded continuously over 3 years.

What is 23.1%?

The number y of hits a new search engine website receives each month can be modeled by y = 4080 ekt

where t represents the number of months the website has been operating. In the websites’s third month, there were 10,000 hits. Find the value of k, and use this result to predict the number of hits the website

will receive after 24 months.

What is k = 0.2988 which is appox. 5,309,734 hits?

The number N of bacteria in a culture is modeled by

N = 100ekt

Where t is the time in hours. If N = 300 when t = 5, estimate the time required for the population to

double in size.

What is 3.15 hours?

Find the exponential model y = aebx

that fits the points (0, 1) and (3, 10)

What is y = e0.7675x