Question

please help me it's urgents my exam is on find the value of log 2 16​

Answer 1

Answer:

The value of log 216 is found to be 2.3343.

Step-by-step explanation:

To get the value of the given log function we will use some properties of the log functions.

formula:  $logx^{n}$ = $nlogx$

log a × b = log a + log b

Therefore firstly we need to find or calculate the prime factorization of the 216.

216 = 2×2×2×3×3×3 = $2^{3}$×$3^{3}$

Now we will put up this in place of 216 in the log function.

∴log 216 = log $2^{3}$×$3^{3}$

⇒log 216 = log$2^{3}$ + log$3^{3}$

⇒log 216 = 3 log 2 + 3 log 3

⇒log 216 = 3 × 0.3010 + 3 × 0.4771

⇒ log 216 = 2.3343

Therefore we get the value of log 216 is 2.3343.