Question

Express 2log 3 - 1/2 log 16 + log 12 as a single logarithm

Answer 1

2log3 - 1/2log16 + log12
We know concept of logarithm,
$\bold{alogn= logn^a}$ use it here,

2log3 = log3² = log9
1/2log16 = log16½ = log(4²)½ = log4

∴ 2log3 - 1/2log16 + log12 = log9 - log4 + log12

Again, use concept $\bold{loga-logb =loga/b}\\\bold{loga+logb=logab}$
∴log9 - log4 + log12 = log9 + log12 - log4
= Log(9 × 12) - log4
= Log108 - log4
= Log 108/4
= Log27

Answer 2

Hello Dear.

Here is the answer---


→→→→→→→→→

Given Logarithms Equation,

                     2log3  -  1/2log16  +  log12

We know,
  n log b = log bⁿ

Thus, 2 log 3 = log 9
         
&      1/2 log 16 = log 16 ¹⁾²
                         = log 4 ² ˣ ¹⁾²
                         = log 4

&   log 12 = log (4 × 3)
                = log 4 + log 3

Now,
  2 log 3 - 1/2 log 16 + log 12
           = log 9 - log 4 + log 4 + log 3
           = log 108 - log 4
           = $log \frac{108}{4}$
           = log 27
           = log 3 ³
           = 3 log 3

Thus, In the simple Logarithms the value of the given equation will be
3 log 3.


→→→→→→→→→→→


Hope it helps.

Have a Marvelous Days.