Question

Which of the following is equivalent to log816? a. 2 b. 1.248 c. 4/3 d. 3/4

Answer 1

Answer:  The correct option is (c) $\dfrac{4}{3}.$

Step-by-step explanation:  We are to select the correct value that is equivalent to the following expression :

$E=\log_8{16}.$

We will be using the following logarithmic properties :

$(i)~\log a^b=b\log a,\\\\(ii)~\log_ab=\dfrac{\log b}{\log a}.$

So, the given expression becomes

$E\\\\=\log_8{16}\\\\\\=\dfrac{\log16}{\log8}\\\\\\=\dfrac{\log2^4}{\log2^3}\\\\\\=\dfrac{4\log2}{3\log2}\\\\\\=\dfrac{4}{3}.$

Thus, the required value is $\dfrac{4}{3}.$

Option (c) is CORRECT.

Answer 2

X=4/3
C 4/3 hope this helped