What to do next?

lemon14 · Mar 22, 2011, 11:21 AM

I came across this exercise and I don't know what to do next (or if I solved it correctly to this point)

$x^{log_3 (x+1)} + (x+1)^{log_3 x} = 2x^2$

$log_3 {x^{log_3 (x+1)}} + log_3 {(x+1)^{log_3 x}} = log_3 {(2x^2)}$

$2 log_3 {x} * log_3 {(x+1)} = log_3 {2} + 2log_3 {x}$

ebaines · Mar 22, 2011, 11:55 AM

You are making the mistake of assuming that if

$<br /> a + b = c<br />$

then
$<br /> log(a) + log(b) = log(c)<br />$

which is not right.

Rather than using brute force I suggest you try a few numbers that look like reasonable candidates. You want things to cancel out, and at first glance it would seem that trying values for x like x = 3, or x=2 may be promising. You can also try x = 1, since 1 raised to a power is always 1 and log of 1 is always 0. Post back with what you get.

Add your answer here.