Question

Find the value of x for which 2 power of x ÷ 2 power of -4 = 45​

Answer 1

$\Large{\bold{\blue{\underline{\red{A}\pink{ns}\green{we}\purple{r:-}}}}}$

$\rm{\mapsto The \: value \: of \: x = {log}_{2}(45) - 4}$

$\Large{\bold{\pink{\underline{\green{G}\purple{iv}\orange{en}\red{:-}}}}}$

$\rm{\leadsto {2}^{x} \div {2}^{-4}= 45}$

$\Large{\bold{\blue{\underline{\red{To}\:\pink{Fin}\green{d}\purple{:-}}}}}$

$\rm{\leadsto The \: value \: of \: x = \: ?}$

$\Large{\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

$\tt{: \implies {2}^{x} \div {2}^{ - 4} = 45}$

$\tt{: \implies log_{2}( {2}^{x} \div {2}^{ - 4}) = log_{2}(45) }$

$\tt{: \implies log_{2} \bigg( {2}^{x} \times \dfrac{1}{ {2}^{ - 4} } \bigg) = log_{2}(45) }$

$\tt{: \implies log_{2}( {2}^{x}) + log_{2} \bigg( \dfrac{1}{ {2}^{ - 4} } \bigg) = log_{2}(45) }$

$\tt{: \implies x log_{2}(2) + log(1) - log_{2}( {2}^{ - 4} ) = log_{2}(45) }$

$\tt{: \implies 1x + log_{2}(1) - log_{2}( {2}^{ - 4} ) = log_{2}(45) }$

$\tt{: \implies 1x + log_{2}(1) - log_{2}( {2}^{ - 4}) = log_{2}(45)}$

$\tt{: \implies x + log_{2}(1) - log_{2}( {2}^{ - 4} ) = log_{2}(45) }$

$\tt{: \implies x + 0 - log_{2}( {2}^{ - 4} ) = log_{2}(45) }$

$\tt{: \implies x - log_{2}( {2}^{ - 4} ) = log_{2}(45) }$

$\tt{: \implies x - ( - 4 log_{2}(2) ) = log_{2}(45) }$

$\tt{: \implies x + 4 log_{2}(2) = log_{2}(45) }$

$\tt{: \implies x + 4 \times 1 = log_{2}(45) }$

$\tt{: \implies x + 4 = log_{2}(45) }$

$\bf{: \implies \underline{ \: \underline{ \red{ \: x = log_{2}(45) - 4 \: }} \: }}$