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OpenStudy (anonymous):
I'm sorry but what does 5^x^2
mean?
OpenStudy (anonymous):
5 raise to the x raise to the second
OpenStudy (anonymous):
\[5^{x^2} = 625^x\]
right?
OpenStudy (anonymous):
\[5^{x^2} = 625^x\]
OpenStudy (anonymous):
that's right
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OpenStudy (anonymous):
take log of both sides and recall that:\[\log(a^b) = b*\log(a)\]
OpenStudy (anonymous):
i know the answer is 0.4, but i don't know why
OpenStudy (anonymous):
take the log of both sides like Euler said,
OpenStudy (anonymous):
\[\log(5^{x^2}) = \log(625^x)\]using rule:\[x^2 \log(5) = x \log(625)\]
use calculator :)
OpenStudy (anonymous):
This isn't simplified
x=2+3√,2−3√
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OpenStudy (anonymous):
I'm building off of Euler comment.
OpenStudy (anonymous):
\[x[xlog(5) - \log(625)] = 0\]answer is x = 0 or
\[xlog(5) - \log(625) = 0\]
\[x = \frac{ \log625 }{ \log5 } = 4\]
OpenStudy (anonymous):
answer is 0, 4 [zero and four] and not 0.4 :)
OpenStudy (anonymous):
\[\text{Log}\left[5^{x^2}\right]\text{=}\text{Log}\left[625^x\right] \]\[x^2 \text{Log}[5]=4 x \text{Log}[5]\]\[x^2 -4 x =0\]\[(x-4) x=0 \]You can take it from here.