# Thread: x = 25 ^ (1 + log(base 5) x)

1. ## x = 25 ^ (1 + log(base 5) x)

Solve for X:

X = 25 ^ (1 + log(base 5) X)

My steps:

Bring the exponent down

log(base 25) X = 1 + log(base 5) X

I am stuck here as I have 2 different bases, log X to base 25 and log X to base 5.

How should I solve this? Thanks.

2. Originally Posted by shenton
Solve for X:

X = 25 ^ (1 + log(base 5) X)

My steps:

Bring the exponent down

log(base 25) X = 1 + log(base 5) X

I am stuck here as I have 2 different bases, log X to base 25 and log X to base 5.

How should I solve this? Thanks.
why did you take log(base25)?

take log(base5) of both sides:

log(base5)X = log(base5)25 ^ (1 + log(base 5) X)

call log(base5) just log, and remember we're working in base 5

=> logx = (1 + logx)log25
=> logx = (1 + logx)2 .................log(base5)25 = 2
=> logx = 2 + 2logx
=> logx = -2
=> 5^-2 = x
=> 1/5^2 = x
=> x = 1/25

3. Here.

4. Originally Posted by ThePerfectHacker
Here.
that's a nice way to do it, very elegant. my way was more mechanical and muscle memory based