Finding the Solution to the Equation 2^x = 12 + 4x

[WeiLoong]

Homework Statement

2^x=12+4x Find x.

Homework Equations

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The Attempt at a Solution

I have tried to change it in form of logarithm xlog2=log4+log3+x and i found that log(3+x) is unexpandable so i was stuck here.

 

[BvU]

Hello Weiloong, welcome to PF !

Your change isn't correctly written: it is true that log(2^x) = x log 2, but for log (12 + 4x) you meant log 4 + log(3+x) and that indeed doesn't help all that much.

Why don't you do some trial and error and see what comes out: x = 1, 2, 3, etc...

 

[Geofleur]

You could also try plotting the left and right sides of the equation and seeing where the curves meet, though that only gives an approximate answer.

 

[berkeman]

Homework Equations

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Isn't the Quadratic Equation relevant here?

 

[SteamKing]

Isn't the Quadratic Equation relevant here?

I don't think so, since the LHS has 2^x rather than x².

 

[berkeman]

I don't think so, since the LHS has 2^x rather than x².

Oops, thanks! I misread it.

 

[HallsofIvy]

That looks like a candidate for the Lambert W function.

 

[ehild]

You can rewrite the equation as x=2^(x-2)-3. Both sides are increasing functions. Plotting them, you can see where the roots are. For positive x, it should be greater than 4. If x is negative, it should be near -3. Trial and error will work :)