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log2 x is the power to which you need to raise 2 to obtain x With this intuitive notion we readily see that log2 16 = the power to which we raise 2 to obtain 16 = 4 and log2 (1/4) = the power to which we raise 2 to obtain 1/4 = 2 However this intuitive approach does not work so well if we want to take log 5 or log2 7 Therefore we will give a new de nition of the logarithm to any base a > 0 which in simple cases coincides with the intuitive notion of logarithm If a > 0 and b > 0 then ln b loga b = ln a EXAMPLE 619

public int LastIndexOf(char value, int startIndex, int count)

TABLE 22-3

Example: If V 0 V, there is no re ected wave and K of the impedance mismatch is represented as at the sending end KS ZS ZO ________ ZS ZO

The Search Methods Offered by String (continued)

If you review the rst few paragraphs of Section 1, you will nd an intuitively appealing de nition of the logarithm to the base 2:

22:

Method public int LastIndexOf(string value, int startIndex, int count) public int LastIndexOf(string value, StringComparison comparisonType) public int LastIndexOf(string value, int startIndex, StringComparison comparisonType) public int LastIndexOf(string value, int startIndex, int count, StringComparison comparisonType) public int LastIndexOfAny(char[ ] anyOf) public int LastIndexOfAny(char[ ] anyOf, int startIndex) public int LastIndexOfAny(char[ ] anyOf, int startIndex, int count) public bool StartsWith(string value) public bool StartsWith(string value, StringComparison comparisonType) public bool StartsWith(string value, bool ignoreCase, CultureInfo culture)

TABLE 22-3

.

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SOLUTION We see that ln 25 5 ln 2 ln 32 = = = 5 ln 2 ln 2 ln 2 Notice that, in this example, the new de nition of log2 32 agrees with the intuitive notion just discussed log2 32 = EXAMPLE 620

meaning no re ections If V is the incident voltage wave traveling down the line and V is the re ected wave traveling up the line caused by the mismatch of the receiving end impedance, VMAX occurs when they reinforce each other to cause a voltage maximum |VMAX| |VMIN| V and V de ned as |V | |V | |V | |V | (B-1) (B-2)

Description Returns the index of the last occurrence of value within the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and running for count elements Returns 1 if value is not found Culture-sensitive searching is used Returns the index of the last occurrence of value within the invoking string How the search is performed is specified by comparisonType Returns 1 if value is not found Returns the index of the last occurrence of value within a range of the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and stopping at zero How the search is performed is specified by comparisonType Returns 1 if value is not found Returns the index of the last occurrence of value within the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and running for count elements How the search is performed is specified by comparisonType Returns 1 if value is not found Returns the index of the last occurrence of any character in anyOf that is found within the invoking string Returns 1 if no match is found Ordinal searching is used Returns the index of the last occurrence of any character in anyOf that is found within the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and stopping at zero Returns 1 if no match is found Ordinal searching is used Returns the index of the last occurrence of any character in anyOf that is found within the invoking string The search proceeds in reverse order, beginning at the index specified by startIndex and running for count elements Returns 1 if no match is found Ordinal searching is used Returns true if the invoking string begins with the string passed in value Otherwise, false is returned Culture-sensitive searching is used Returns true if the invoking string begins with the string passed in value Otherwise, false is returned How the search is performed is specified by comparisonType Returns true if the invoking string begins with the string passed in value Otherwise, false is returned If ignoreCase is true, the search ignores case differences Otherwise, case differences matter The search is conducted using the cultural information passed in culture.

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