Evaluate log base 2 4^5
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log base 2 with 4^5
(log a^m=m log a)
so,
5 log base 2 with 4
5 log base 2 with 2^2
(log a^m=m log a)
5×2 log base 2 with 2
10 log base 2 with 2
(log base a with a =1)
10×1=10
Verified answer
Answer:
[tex]\boxed{\bf\: log_{2}( {4}^{5} ) = 10 \: } \\ [/tex]
Formulae Used:
[tex] \sf \: log_{x}( {y}^{n} ) = n log_{x}(y) \\ [/tex]
[tex] \sf \: log_{x}(x ) = 1 \\ [/tex]
Step-by-step explanation:
Given expression is
[tex] \sf \: log_{2}( {4}^{5} ) \\ [/tex]
[tex] \sf \: = \: 5log_{2}(4 ) \\ [/tex]
[tex] \sf \: = \: 5log_{2}( {2}^{2} ) \\ [/tex]
[tex] \sf \: = \: 5 \times 2log_{2}(2) \\ [/tex]
[tex] \sf \: = \: 10 \times 1 \\ [/tex]
[tex] \sf \: = \: 10 \\ [/tex]
Hence,
[tex]\implies\sf\:\boxed{\bf\: log_{2}( {4}^{5} ) = 10 \: } \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information:
[tex]\begin{gathered}\: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: Formulae}}}} \\ \\ \bigstar \: \bf{ log_{x}(x) = 1}\\ \\ \bigstar \: \bf{ log_{x}( {x}^{y} ) = y}\\ \\ \bigstar \: \bf{ log_{ {x}^{z} }( {x}^{w} ) = \dfrac{w}{z} }\\ \\ \bigstar \: \bf{ log_{a}(b) = \dfrac{logb}{loga} }\\ \\ \bigstar \: \bf{ {e}^{logx} = x}\\ \\ \bigstar \: \bf{ {e}^{ylogx} = {x}^{y}}\\ \\ \bigstar \: \bf{log1 = 0}\end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]