Question

5^x^2=625^x. solve the equation

Answer 1

I'm sorry but what does 5^x^2
mean?

Answer 2

5 raise to the x raise to the second

Answer 3

\[5^{x^2} = 625^x\]
right?

Answer 4

\[5^{x^2} = 625^x\]

Answer 5

that's right

Answer 6

take log of both sides and recall that:\[\log(a^b) = b*\log(a)\]

Answer 7

i know the answer is 0.4, but i don't know why

Answer 8

take the log of both sides like Euler said,

Answer 9

\[\log(5^{x^2}) = \log(625^x)\]using rule:\[x^2 \log(5) = x \log(625)\]
use calculator :)

Answer 10

This isn't simplified
x=2+3√,2−3√

Answer 11

I'm building off of Euler comment.

Answer 12

\[x[xlog(5) - \log(625)] = 0\]answer is x = 0 or

\[xlog(5) - \log(625) = 0\]
\[x = \frac{ \log625 }{ \log5 } = 4\]

Answer 13

answer is 0, 4 [zero and four] and not 0.4 :)

Answer 14

\[\text{Log}\left[5^{x^2}\right]\text{=}\text{Log}\left[625^x\right] \]\[x^2 \text{Log}[5]=4 x \text{Log}[5]\]\[x^2 -4 x =0\]\[(x-4) x=0 \]You can take it from here.