Thread: Logarithm problem

solve x, I have really struggled with this.

30,000=0.1(60,000)^x+0.9(10,000)^x
For the life of me i cant remember my a-level maths!
Any help is very much appreciated!
Ben

Start by taking ln of both sides. Then you can use a property of logarithms to bring x down from its perch.

ln(30000)=o.1x*ln(60000)+0.9x*ln(10000)

Factor out x, and bring some terms together.

ln(30000)/(0.1*ln(60000)+0.9*ln(10000))=2x

x=ln(30000)/2*(o.1*ln(60000)+0.9*ln(10000))

This can further be reduced, but I'll leave that up to you.


Best,


-F

Thank you! Just still very confused as to what to do next, I had got to that point but couldn't get it any further, sorry i should have explained in the question.!
Ben

Originally Posted by FlacidCelery

Start by taking ln of both sides. <<< better not!
Then you can use a property of logarithms to bring x down from its perch.

ln(30000)=o.1x*ln(60000) + 0.9x*ln(10000)

The +-sign idicates a product in the original equation which isn't there.

Originally Posted by bojker26

solve x, I have really struggled with this.

30,000=0.1(60,000)^x+0.9(10,000)^x
For the life of me i cant remember my a-level maths!
Any help is very much appreciated!
Ben

The only way I see to solve the equation is using an iterative method like Newton:

Construct a function f:



and calculate the zeros of this function.



I used and after few steps got a result of

Originally Posted by FlacidCelery

Start by taking ln of both sides. Then you can use a property of logarithms to bring x down from its perch.

ln(30000)=o.1x*ln(60000)+0.9x*ln(10000)

This is incorrect. log(ax+ by) is NOT alog(x)+ blog(y) so

Earboth's numerical method is probably the best you can do.

Factor out x, and bring some terms together.

ln(30000)/(0.1*ln(60000)+0.9*ln(10000))=2x

x=ln(30000)/2*(o.1*ln(60000)+0.9*ln(10000))

This can further be reduced, but I'll leave that up to you.


Best,


-F