Question

homework.derivita.com
convert each equation into its equivalent
logarithmic form.
a) $2^4 = 16$
$\log_2(4) = 16$
$\log_4(16) = 2$
$\log_2(16) = 4$
none of the above
b) $5^2 = 25$
$\log_5(25) = 2$
$\log_2(25) = 5$
$\log_5(2) = 25$
none of the above
c) $3^2 = 9$
$\log_3(9) = 2$
$\log_2(9) = 3$

Explanation:

Part (a)

Step1: Recall the exponential - logarithmic conversion formula

The formula for converting an exponential equation \(a^{b}=c\) (where \(a>0,a
eq1\)) to its logarithmic form is \(\log_{a}(c)=b\).

Step2: Apply the formula to \(2^{4} = 16\)

In the equation \(2^{4}=16\), we have \(a = 2\), \(b = 4\) and \(c = 16\). Using the conversion formula \(\log_{a}(c)=b\), we substitute the values: \(\log_{2}(16)=4\).

Step1: Recall the exponential - logarithmic conversion formula

The formula for converting an exponential equation \(a^{b}=c\) (where \(a > 0,a
eq1\)) to its logarithmic form is \(\log_{a}(c)=b\).

Step2: Apply the formula to \(5^{2}=25\)

In the equation \(5^{2}=25\), we have \(a = 5\), \(b = 2\) and \(c = 25\). Using the conversion formula \(\log_{a}(c)=b\), we substitute the values: \(\log_{5}(25)=2\).

Step1: Recall the exponential - logarithmic conversion formula

The formula for converting an exponential equation \(a^{b}=c\) (where \(a>0,a
eq1\)) to its logarithmic form is \(\log_{a}(c)=b\).

Step2: Apply the formula to \(3^{2}=9\)

In the equation \(3^{2}=9\), we have \(a = 3\), \(b = 2\) and \(c = 9\). Using the conversion formula \(\log_{a}(c)=b\), we substitute the values: \(\log_{3}(9)=2\).

Answer:

C. \(\log_{2}(16)=4\)

Part (b)