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solve 2^x=8

 May 9, 2014

Best Answer 

 #2
avatar+1006 
+8

Think of how many times 2 needs to be multiplied in order to get eight.

 

2 x 2 = 4

4 x 2 = 8

 

Therefore, since 3 '2's were used, x = 3

 May 9, 2014
 #1
avatar+91 
+8

2^3 = 8. x is equal to 3

 #2
avatar+1006 
+8
Best Answer

Think of how many times 2 needs to be multiplied in order to get eight.

 

2 x 2 = 4

4 x 2 = 8

 

Therefore, since 3 '2's were used, x = 3

GoldenLeaf May 9, 2014
 #3
avatar
+5
  1. $$2^x=8\quad|\quad \ln{}$$
  2. $$\ln{(2^x)}=\ln(8)$$
  3. $$x*\ln{2}=\ln{8}$$
  4. $$x=\frac{\ln{8}}{\ln{2}}=\frac{\ln{(2*2*2)}}{\ln{2}}=\frac{\ln{2}+\ln{2}+\ln{2}}{\ln{2}}=\frac{\ln{2}}{\ln{2}}+\frac{\ln{2}}{\ln{2}}+\frac{\ln{2}}{\ln{2}}=1+1+1=3$$
  5. $$\boxed{x=3}$$

 

S.

 May 9, 2014
 #4
avatar+129849 
+5

We can also equate bases to solve this.

2x = 8

2x = 23

So, x = 3.

 May 9, 2014

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