Question

Evaluate each expression. Log327 = log121 = log5 1 25 = log2128 =

Answer 1

Answer:

the second part to the question is

a,c,d

Step-by-step explanation:

Answer 2

Expressions can be expressed using logarithms

The results of the expression are:

$\mathbf{log_3(27) = 3}$

$\mathbf{log_{11}(121) = 2}$

$\mathbf{log_{5}(125) = 3}$

$\mathbf{log_{2}(128) = 7}$

$\mathbf{(a)\ log_3(27)}$

Express 27 as 3^3

$\mathbf{log_3(27) = log_3(3^3)}$

Apply law of logarithm

$\mathbf{log_3(27) = 3log_3(3)}$

So, we have:

$\mathbf{log_3(27) = 3\times 1}$

$\mathbf{log_3(27) = 3}$

$\mathbf{(b)\ log_{11}(121)}$

Express 121 as 11^3

$\mathbf{log_{11}(121) = log_{11}(11^2)}$

Apply law of logarithm

$\mathbf{log_{11}(121) = 2log_{11}11}$

So, we have:

$\mathbf{log_{11}(121) = 2\times 1}$

$\mathbf{log_{11}(121) = 2}$

$\mathbf{(c)\ log_{5}(125)}$

Express 125 as 5^3

$\mathbf{log_{5}(125) = log_5(5^3)}$

Apply law of logarithm

$\mathbf{log_{5}(125) = 3log_5(5)}$

So, we have:

$\mathbf{log_{5}(125) = 3\times 1}$

$\mathbf{log_{5}(125) = 3}$

$\mathbf{dc)\ log_{2}(128)}$

Express 128 as 2^7

$\mathbf{log_{2}(128) = log_2{2^7}}$

Apply law of logarithm

$\mathbf{log_{2}(128) = 7log_2{2}}$

So, we have:

$\mathbf{log_{2}(128) = 7\times 1}$

$\mathbf{log_{2}(128) = 7}$

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