Question

log10 xy =2 then find value of xy ​

Answer 1

Step-by-step explanation:

log10(xy) = log10(x/y) + 2log102

or, log10(xy) = log10(x/y) + log(102)^2 or, log10(xy) = log10(x/y x (102)^2)

or, xy = ((102)^2). x)/y

or, y = ((102)^2)/y (eliminating x on both sides)

or, y^2 = (102)^2

or, y = 102

now, log10(xy) = 2

or, xy = 100

or x = 50/51

Answer 2

Answer:

Concept:

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which a fixed number, base b, must be raised in order to create a specific number x, is represented by the logarithm of that number.

Step-by-step explanation:

Given:

$log_{10} ( xy) =2$

To find:

Value of $xy$

Solution:

• The logarithmic number has an exponent and a power attached to it, thus if $p^{x}=m$, it is equivalent to $log_{p} m=x$.
• As a result, it is essential that we also understand exponent law. For instance, the logarithm of $10,000$ to base $10$ is $4$, since the power of ten that must be increased to get $10,000$ is $4$, making $log_{10}10000=4$.
• By product rule, A product's log is equal to the product of its two logs.

                                           $log_{x}p \times log_{x}q=log_{x}pq$

• The given statement can be written as,

                                             $log_{10} xy =log_{10} x \times log_{10} y = 2$

• By property of logarithms,

              if   $log_{x} p=m$  then $p=x^{m}$     ⇒  A

• Using the property stated by A, the given statement can be written as

               $log_{10} xy = 2$  

                       $xy=10^{2}$

                       $xy=100$

Hence, value of $xy=100$

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