Express as a single logarithm.
2log3-1/2log16+log12
Answers
2log3 - 1/2log16 + log12
We know concept of logarithm,
use it here,
2log3 = log3² = log9
1/2log16 = log16½ = log(4²)½ = log4
∴ 2log3 - 1/2log16 + log12 = log9 - log4 + log12
Again, use concept
∴log9 - log4 + log12 = log9 + log12 - log4
= Log(9 × 12) - log4
= Log108 - log4
= Log 108/4
= Log27
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 27
= log 3 ³
= 3 log 3
Thus, In the simple Logarithms the value of the given equation will be
3 log 3.