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Mathematics - Logarithmic and Exponential Functions

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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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Solution Summary

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

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 ...

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