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Exponential equation

  • Thread starter DTA
  • Start date
  • #1
DTA
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Homework Statement



Solve for x:

4x+7=18

Homework Equations



It becomes 4x=11

The Attempt at a Solution



I have no idea where to go from here. We never had a problem with such an immovable number such as 11 to work with. Calculators are not allowed to be used either.
 

Answers and Replies

  • #2
2,967
5
Use the definition of a logarithm.
 
  • #3
DTA
6
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Okay, I think I'm on the right track but I'm still not sure where to go with this:

4log411= ?
 
  • #4
2,967
5
Okay, I think I'm on the right track but I'm still not sure where to go with this:

4log411= ?
For logarithms it is always true that:

[tex]
a^{x} = b \Leftrightarrow x = \log_{a}{b}, \; a, b > 0, \; a \neq 1
[/tex]

From here we have the fundmanetal property of logarithms:

[tex]
a^{\log_{a} b} = b
[/tex]
 
  • #5
LCKurtz
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It becomes 4x=11
Take the log of both sides to any base and solve for x. It doesn't have to be base 4 and if you were after a decimal approximation you would likely want to use base e or base 10.
 
  • #6
DTA
6
0
Okay, so I attempted a change of base and got this:

ln11/ln4 ~ 1.729

Is this how it eventually would end up?


Thanks for all your help! Logarithms are just driving me nuts for some reason
 
  • #7
2,967
5
yes.
 

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