Question

Find the answer of the question​

Answer 1

Answer:

20 is the correct answer

➳To Find:

• Value of $2^{2+\log_{2}{5} }$

☸Solution☸

We know that(Logarithmic properties),

• $\bf{a^{\log_{a}{n} }=n{,where\:a>0,a\neq {1}}}$
• $\bf{\log_{a}{m^{n} }=n\log_{a}{m}{,where\:a>0,a\neq {1}}}$
• $\bf{{\log_{a}{a}=1}{,where\:a>0,a\neq {1}}}$
• $\bf{\log_{2}{4}=\log_{2}{2^{2} }=2\log_{2}{2}=2}$
• $\bf{{\log_{a}{m}+\log_{a}{n}=\log_{a}{(m\times n)}}{,where\:a>0,a\neq {1}}}$

Now,

$\longrightarrow\sf{2^{2+\log_{2}{5} }}$

After changing 2 into $\bf{\log_{2}{4}}$, we get

$\longrightarrow\sf{2^{\log_{2}{4}+\log_{2}{5} }}$

$\longrightarrow\sf{2^{\log_{2}{\red{(4\times5)}} }}$

$\longrightarrow\sf{2^{\log_{2}{\red{(20)}} }}$

$\longrightarrow\sf{\purple{20}}$

☛Hence, the value of $2^{2+\log_{2}{5} }$ is $\bf{\green{20}}$.