Question

find the solution of the exponential equation
7^(x/2)=5^(1-x)

Answer 1

\[7^{\frac{ x }{ 2 }}=5^{1-x}\]

Answer 2

\(7^{x/2}=5^{1-x}\)

SNAP!!

Answer 3

i am stuck here \[x(\frac{ 1 }{2 }\ln 7+\ln 5)=\ln 5\]

Answer 4

\[x(a)=b\\x=\frac{b}{a}\]

Answer 5

\[x=\frac{ \ln 5 }{ \frac{ 1 }{ 2 }\ln 7+\ln 5 }\]

Answer 6

for some reason doesn't feel right..

Answer 7

\[\frac{1}{2}\ln7+\ln5=\ln \sqrt{7}+\ln5=\\ln(5\sqrt{7})\\x=\frac{\ln5}{\ln(5\sqrt{7})}\]

Answer 8

i am so stupid -.-.. Thank you!!