Solve Algebraically: (x+1)^y = a and x^y = b

[murshid_islam]

is there any way to solve the following set of equations algebraically

$$(x+1)^y = a$$

$$x^y = b$$

 

[eaboujaoudeh]

yes there is...now you try it, and tell us how far you get

 

[whatta]

cough. how many more you have there?

 

[eaboujaoudeh]

i take back what i said...what on Earth is that equation :)

 

[whatta]

Hmmm... it appears that if there is such y that $$b^(1/y) = a^(1/y) - 1$$, any x will satisfy these equations?

 

[murshid_islam]

Hmmm... it appears that if there is such y that $$b^(1/y) = a^(1/y) - 1$$, any x will satisfy these equations?

maybe you mean if there is such y that $$b^{\frac{1}{y}} = a^{\frac{1}{y}} - 1$$, any x will satisfy these equations?

then it also appears that if there is such x that $$\frac{\ln a}{\ln (x+1)} = \frac{\ln b}{\ln x}$$, any y will satisfy these equations.

cough. how many more you have there?

lol. i have no more. i got the equation in the thread you mention from
(x+1)^y = 216
x^y = 125

 

[whatta]

hmm. no it's me who takes back what I said. "any" x will not do.