Evaluating Lograrithms

The Problem

Evaluate each logarithm.

a). log base 2 of 8

b). log bas 5 of 1 25th

c). log base 7 of 49

d). natural log of e to the -7 power

The calculator can be used to evaluate each of these logarithms. Since the calculator directly evaluates only common logarithms (base 10) and natural logarithms (base e), the change of base formula is needed for parts a, b, and c of the problem above.

Change of Base Formula: log base b of x equals log x over log b

Solution to part a:

a). Rewite log base 2 of 8 equals log 8 over log 2. To enter this expression in the calculator, press ALPHA Y=. Select 1:n/d, the enter LOG 8), down arrow and LOG 2). Then press ENTER. See the results below.

Thus log base 2 of 8 = 3

b). Rewrite . To enter this expression, press ALPHA Y=. Select 1:n/d, the press LOG and press ALPHA Y=. Select 1:n/d. Type 1, down arrow and 25 ) down arrow and type LOG 5). The press ENTER. See the results below.

Thus log bas 5 of 1 25th = -2.

 

c). Rewrite . To enter this expression press ALPHA Y=. Select 1:n/d, then press LOG 49), then down arrow and LOG 7). Then press ENTER. See the results below.

Thus log base 7 of 49= 2.

 

d). Since the base of this logarithm is e, enter the expression by pressing LN 2nd, then LN -7)). Then press ENTER.

Thus natural log of e to the -7 power = -7.


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