# Thread: Logarithms (^^,)

1. ## Logarithms (^^,)

Hiii

could someone help me ?!

I have this problem and I solved it but I'm not sure if my answer is correct

so I just want you to tell me if it's correct or not

and if it wasn't correct .. maybe you can help me find the correct answer

well .. ok

log { base 4 } of x = 25 log { base x } of 4

log { base 4 } of x = 25/[log { base 4 } of x]

log { base 4 } of x - 25/[log { base 4 } of x] = 0

let' say that K = log { base 4 } of x

K - 25/K = 0

(K)K - (K)25/K = (K)0

(K^2) - 25 = 0

K^2 = 25

K = 5

log { base 4 } of x = 5

x = 4^5

x = 1024

is my answer correct ?!

2. You missed a solution!
$(\log_4x)^2=25\Rightarrow \log_4x=\pm 5$.
If $\log_4x=5\Rightarrow x=4^5=1024$.
If $\log_4x=-5\Rightarrow x=4^{-5}=\frac{1}{1024}$

3. Thank u so much for ur help

so

x = 1024

or

x = 1/1024