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33554432=x^5

Guest Jun 9, 2015

Best Answer 

 #4
avatar+20033 
+10

33554432=x^5   x = ?

$$\small{\text{$
\rm{The~prime~ factorization~ of~} \mathbf{ 33554432 = 2^{25} }
$}} \\
\small{\text{$
\rm{so~we~have~} \mathbf{ 2^{25} = x^5}
$}} \\
\small{\text{$
\rm{or~} \mathbf{ 2^{5\cdot 5} = x^5}
$}} \\
\small{\text{$
\rm{or~} \mathbf{ (2^5)^5 = (x)^5} \qquad | \qquad \rm {comparing~coefficient}
$}} \\
\small{\text{$
\rm{so~} \mathbf{ (2^5) = x}
$}} \\
\small{\text{$
\rm{or~} \mathbf{ 32 = x}
$}} \\$$

heureka  Jun 9, 2015
 #1
avatar+93691 
+5

Raise each side to te power of 1/5

Melody  Jun 9, 2015
 #2
avatar+7493 
+5

Hallo anonymous!

 

33554432=x^5

 

ln 33554432  = 5 * ln x

ln x = (ln 33554432) / 5 = 3,4657359028
x = e^3,4657359028
 
x = 32
 
Grüße von  :- )
asinus  Jun 9, 2015
 #3
avatar+93691 
+5

Thanks asinus 

You have done it the really long way.  You only need to use logs when you are finding a power.

The best way to do this problem is to just raise both sides to the power of 1/5

 

$$\\33554432=x^5\\\\
x^5=33554432\\\\
(x^5)^{1/5}=33554432^{1/5}\\\\
x=33554432^{1/5}\\\\$$

 

$${{\mathtt{33\,554\,432}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{5}}}}\right)} = {\mathtt{32}}$$

Melody  Jun 9, 2015
 #4
avatar+20033 
+10
Best Answer

33554432=x^5   x = ?

$$\small{\text{$
\rm{The~prime~ factorization~ of~} \mathbf{ 33554432 = 2^{25} }
$}} \\
\small{\text{$
\rm{so~we~have~} \mathbf{ 2^{25} = x^5}
$}} \\
\small{\text{$
\rm{or~} \mathbf{ 2^{5\cdot 5} = x^5}
$}} \\
\small{\text{$
\rm{or~} \mathbf{ (2^5)^5 = (x)^5} \qquad | \qquad \rm {comparing~coefficient}
$}} \\
\small{\text{$
\rm{so~} \mathbf{ (2^5) = x}
$}} \\
\small{\text{$
\rm{or~} \mathbf{ 32 = x}
$}} \\$$

heureka  Jun 9, 2015

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