Exponential simultaneous equation with powers

[acu04348]

Hi there,Struggling with this problem, anyone know how this might be solved?

(e^(r-0.04)^(5/12))(0.9463) = (e^(r-0.04)^(11/12))(0.95152)

and solve for r

Ans: r~2.90%

Would really appreciate it!

 

[Mark44]

Hi there,Struggling with this problem, anyone know how this might be solved?

(e^(r-0.04)^(5/12))(0.9463) = (e^(r-0.04)^(11/12))(0.95152)

and solve for r

Ans: r~2.90%

Would really appreciate it!

It's hard to tell for certain what you're working with. Is this it?
$$0.9463(e^{r - .04})^{5/12} = .95152(e^{r - .04})^{11/12}$$

If so, when you raise an exponent to a power, the exponents multiply, so the above can be rewritten as
$$0.9463e^{(5/12)(r - .04)} = .95152e^{(11/12)(r - .04)}$$

Now take the natural log of both sides.

 

[acu04348]

Thank you Mark44.