# If ${\log _2}x = 3$, then find the value of $x$

Answer

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Hint: - Use logarithmic property ${\log _a}b = \dfrac{{\log b}}{{\log a}}$

Given:

${\log _2}x = 3....................\left( 1 \right)$

As we know ${\log _a}b = \dfrac{{\log b}}{{\log a}}$

Therefore from equation (1)

$

\dfrac{{\log x}}{{\log 2}} = 3 \\

\Rightarrow \log x = 3\log 2 \\

$

Now we know $a\log b = \log {b^a}$

Therefore above equation is written as

$ \Rightarrow \log x = 3\log 2 = \log {2^3} = \log 8$

So, on comparing $x = 8$

So, this is the required answer.

Note: - In such types of questions the key concept we have to remember is that always remember the property of logarithmic which is stated above, then using this property simplify the given problem we will get the required answer.

Given:

${\log _2}x = 3....................\left( 1 \right)$

As we know ${\log _a}b = \dfrac{{\log b}}{{\log a}}$

Therefore from equation (1)

$

\dfrac{{\log x}}{{\log 2}} = 3 \\

\Rightarrow \log x = 3\log 2 \\

$

Now we know $a\log b = \log {b^a}$

Therefore above equation is written as

$ \Rightarrow \log x = 3\log 2 = \log {2^3} = \log 8$

So, on comparing $x = 8$

So, this is the required answer.

Note: - In such types of questions the key concept we have to remember is that always remember the property of logarithmic which is stated above, then using this property simplify the given problem we will get the required answer.

Last updated date: 20th Sep 2023

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