Question

solve \[3^{2x}-5(3^x)=-6\]

Answer 1

solve
\[u^2-5u+6=0\] by factoring, then replace \(u\) by \(5^x\) and solve for \(x\)

Answer 2

\[u^2-5u+6=0\]
\[(u-2)(u-3)=0\]
\[u=2,u=3\]
\[5^x=2\iff x=\log_5(2)\]
\[5^x=3\iff x=\log_5(3)\]

Answer 3

the answer is supposed to be 1 or 0.631

Answer 4

when i got (u-2)(u-3)=0
i did
u=2, u=3
\[3^x=3,3^x=2\]\[x=1,x=\log(2)/\log(3)\]

Answer 5

well i am an idiot, it said \(3^x\) not \(5^x\) so i screwed up
it should be \(3^x=3\) so \(x=1\) or
\[3^x=2\] so \(x=\frac{\ln(2)}{\ln(3)}\)

Answer 6

LOL its okay. thank you for your help