Question

If 25 power y = 8 power x,
and 125 power y = 4 power (x-1),
Find "x".

Answer 1

are you saying 25^8^x and 125^4^(x-1)?

Answer 2

No

Answer 3

25 power y. what does that mean then if it doesn't mean to the power of (^)

Answer 4

is it 25^y = 8^x
and
125^y = 4^(x-1)

Answer 5

\[25^{y} = 8^{x}\]\[yln25 = xln8\]\[y = \frac{x \ln8}{\ln25}\]
and \[125^{y} = 4^{x-1}\]\[y \ln125 = (x-1) \ln4\]\[y = \frac{(x-1)\ln4}{\ln125}\] Substitute for y so the two equations are equal:\[\frac{x \ln8}{\ln25} = \frac{(x-1)\ln4}{\ln125}\]Then solve for x:\[x \ln8 \ln125 = (x-1)\ln4 \ln25\]\[x \ln8 \ln125 = x \ln4 \ln25 -\ln4 \ln25 \]\[ (\ln8 \ln125 - \ln4 \ln25)x = -\ln4 \ln25 \]\[x = \frac{ -\ln4 \ln25 }{ (\ln8 \ln125 - \ln4 \ln25)}\]\[x = \ln4 = 1.38629\]

Answer 6

\[25^y=8^x\Rightarrow 5^{2y}=2^{3x}\]
\[125^y=4^{x-1}\Rightarrow5^{3y}=2^{2(x-1)}\]

\[(5^{2y})^{3/2}=(2^{3x})^{3/2}\Rightarrow5^{3y}=2^{9x/2}\]

\[2^{2(x-1)}=2^{9x/2}\Rightarrow2(x-1)=9x/2\Rightarrow4x-4=9x\Rightarrow x=\frac{-4}{5}\]