Question

harsha said if a=2log5,b=5log2 then a=b.Do you agree?justify u r answer

Answer 1

Answer:

No she is incorrect with her observation.

( as $a=\log 25$ is not equal to $b=\log 32$ )

Step-by-step explanation:

We are given that:

$a=2\log 5$ and $b=5\log 2$

We know by the property of the logarithmic function that:

$m\log n=\log n^m$

Where m and n are real numbers.

So from the expression of a and b we can represent them as:

$a=\log 5^2$ and $b=\log 2^5$

this means we can write them as:

$a=\log 25$ and $b=\log 32$

( since $5^2=5\times 5=25\\and 2^5=2\times 2\times 2\times 2\times 2=32$ ).

Hence, a≠b.

Hence, Harsha is incorrect.