Question

Write 2logx+3log 4+log2 as a single logarithm

Answer 1

Step-by-step explanation:

Given:-

2logx+3log 4+log2

To find :-

Write 2logx+3log 4+log2 as a single logarithm ?

Solution :-

Given that :

2logx+3log 4+log2

We know that

log a^m = m log a

=> log x² + log 4³ + log 2

=> log x² + log (4×4×4) + log 2

=> log x² + log 64 + log 2

We know that

log ab = log a + log b

=> log (x²×64×2)

=> log 128x²

Answer:-

The single logarithm of the given problem is

log (128x²)

Used formulae:-

• log a^m = m log a

• log ab = log a + log b

Points to know :-

• a^x =N => log N (a) = x

Where (a) is the base

• log a/b = log a - log b

• log a (a) = 1

• log 1 = 0

• Common logarithms and Natural logarithms are the two types .

• Common logarithms has base 10

• Natural logarithms has base e

• e = 2.718...

• Logarithms are introduced by John Naepier.