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2 to the power of x is 2048, what is x

 Jun 12, 2015

Best Answer 

 #2
avatar+26387 
+5

2 to the power of x is 2048, what is x

 

$$\small{\text{$
\begin{array} {rcl}
2^x &=& 2048 \qquad | \qquad \ln()\\\\
\ln{(2^x)} &=& \ln{(2048)} \\\\
x\cdot \ln{(2)} &=& \ln{(2048)} \\\\
x &=& \dfrac{ \ln{(2048)} } { \ln{(2)} } \\\\
x &=& \dfrac{ 7.62461898616 } { 0.69314718056} \\\\
\mathbf{x} &\mathbf{=}& \mathbf{11} \\\\
\end{array}
$}}$$

 

 Jun 12, 2015
 #1
avatar+26387 
0
heureka Jun 12, 2015
 #2
avatar+26387 
+5
Best Answer

2 to the power of x is 2048, what is x

 

$$\small{\text{$
\begin{array} {rcl}
2^x &=& 2048 \qquad | \qquad \ln()\\\\
\ln{(2^x)} &=& \ln{(2048)} \\\\
x\cdot \ln{(2)} &=& \ln{(2048)} \\\\
x &=& \dfrac{ \ln{(2048)} } { \ln{(2)} } \\\\
x &=& \dfrac{ 7.62461898616 } { 0.69314718056} \\\\
\mathbf{x} &\mathbf{=}& \mathbf{11} \\\\
\end{array}
$}}$$

 

heureka Jun 12, 2015

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