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Mathematics - Logarithmic and Exponential Functions

Practice Questions on Logarithmic and Exponential Functions

[See the Attached Questions File]

Evaluate the logarithm:

log4(1/16)

Evaluate the logarithm:

log10(0.01)

Evaluate the logarithm:

log1/2(5)

Sketch the graph of the function and identify the vertical asymptote:

f(x) = -2 + log3x

Use the properties of logarithms to expand the expression:

Use the properties of logarithms to condense the expression:
4(1 + ln x + ln x)
Use the properties of logarithms to condense the expression:
ln (x + 4) - 3 ln x - ln y
Solve the equation:
3^x=500
Find the value of this?
100e^-0.6=

Solve the equation:
2log4 x -log4(x-1)=1

A deposit of $5000 is placed in a savings account for 2 years. The interest for the account is compounded continuously. At the end of 2 years, the balance in the account is $5751.37. What is the annual interest rate for this account?

Find the annual interest rate:
Principal Balance Time Compounding
$5000 $15,399.30 15 years Daily

. Find the annual interest rate:
Principal Balance Time Compounding
$7500 $15,877.50 15 years Continuous

Find the effective yield:
Rate Compounding
5.5% Daily

$ 100 becomes 100[1 + 0.055/365]^365 in one year. This evaluates to $ 105.65 in one year. Thus, interest earned is $ 5.65. Yield = interest/investment = 5.65/100 = 0.056
in one year.

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Attachments

Solution Preview

Please see attached file for solutions to the Practice Questions on Logarithmic and Exponential
Functions.

Evaluate the logarithm:

= log (1/16) / log 4 = log [4^-2] / log 4 = -2.log 4 / log 4 = -2.

Evaluate the logarithm:

= log 0.01 / log 10 = log [10^-2] / log 10 = -2.log 10/log 10 = -2.

Evaluate the logarithm:

= log 5 / log (1/2) = log 5 / log [2^-1] = log 5 / -1.log 2 = - log 5 / log 2 = - 2.32.
Sketch the graph of the function and identify the vertical asymptote:

The graph is shown below. The vertical asymptote is the y - axis, whose equation
is x = 0. [Go and see the next page if required].

Use the properties ...

Solution Summary

Complete, Neat and Step-by-step Solutions to the Practice Questions are provided in the attached file.

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