How to solve an exponential unknown

[EconStudent]

Hi all,

How do I solve for x in the following

36806(1.022)^x=5955(1.073)^x

Thanks

 

[mmm4444bot]

Is this an exercise from some math course? If so, are there any instructions?

As I am not savvy to your situation, I'll simply guess that you have technology available.

Graph both functions together in an appropriate window, and then zoom-in on the intersection point to some desired precision.

Hint:

Restricted domain [30, 45]
Restricted range [50000, 100000]

:cool:

 

[tkhunny]

Let's see your work.

With logarithms, this is an eyeball problem.

 

[EconStudent]

Thanks

But how do I apply logs to both sides to get the linear equation?

 

[EconStudent]

Is this correct

ln(36806) + x(Ln1.022) = ln (5955) + x(ln1.073)

therefore x = ln(5955/36806) /ln(1.022/1.073)

x=37.4

???

 

[wjm11]

Is this correct

ln(36806) + x(Ln1.022) = ln (5955) + x(ln1.073)

therefore x = ln(5955/36806) /ln(1.022/1.073)

x=37.4

???

Test your answer; plug it into your original equation.