Question

prove that : log 2 log√2 log 9 by √3 = 2​

Answer 1

Answer : 1

Step-by-step explanation:

To evaluate your expression, I just need to use three simple points about logarithms, namely:

log(1)=0

log(a/b)=log(a)−log(b)

logn(n)=1

Using point 2 to rewrite your expression, we have:

[log(1)−log(2)]+[log(2)−log(3)]+...+[log(8)−log(9)]+[log(9)−log(10)]

=log(1)−log(10)

Using point 2 to rewrite your expression, we have:

[log(1)−log(2)]+[log(2)−log(3)]+...+[log(8)−log(9)]+[log(9)−log(10)]

=log(1)−log(10)

Using point 2, this simplifies to: −log(10)

The actual answer depends on what base logarithm you are using. I will assume that you are using common logs (aka decimal logs or base-10 logs), in which case, from point 3, the expression reduces to −1