Solve for X : ((3)/(5))^(x)=7^(1-x)

Question

lgbasallote · Answer

$$\huge \frac{3}{5^x} = 7^{1-x}$$
is that the question?

lgbasallote · Answer

or is it $$\huge \left(\frac 35 \right)^x = 7^{1-x}$$

anonymous · Answer

the second one

anonymous · Answer

didnt help

anonymous · Answer

split the left side, and then take the log of both sides

anonymous · Answer

$$ln(3^x)-ln(5^x)=ln(7^{1-x})$$

anonymous · Answer

pull out the x to the front

$$xln(3)-xln(5)=(1-x)ln(7)$$

anonymous · Answer

distribute the right side

\[xln(3)-xln(5)=ln(7)-xln(7)

anonymous · Answer

$$xln(3)-xln(5)=ln(7)-xln(7)$$

anonymous · Answer

get all the x terms on one side and factor an x out

anonymous · Answer

can you finish this

anonymous · Answer

still stuck >.<

waleed_imtiaz · Answer

Did that help ?

anonymous · Answer

$$x \ln (3/5)=(1-x)\ln 7$$
$$x \ln 3-x \ln 5=\ln 7-xln 7$$
like terms
$$x \ln 3-xln 5+x \ln 7=\ln 7$$
$$x \ln (3*7/5)=\ln 7$$
$$x=\ln (21/5)/\ln 7$$

anonymous · Answer

Alternatively
$$(3/5)^x=7/7^x$$
$$(3/5)^x(7^x)=7$$

$$(3/5*7)^x=7$$
$$x=\log_{21/7}7 $$
which is also
$$x \ln (3/5*7)=\ln 7$$

anonymous · Answer

That's not one of my choices. my choices are

A. No real solutions
B. − 5.76
C. − 0.8599
D. 1.356
E. None of the above

anonymous · Answer

(3/5)^x = 7^(1 - x)
 x log (3/5) = (1 - x ) log 7
 x log (3/5) = log 7 - x log 7
 x [ log (3/5) + log 7 ] = log 7
 x [ log (21/5) ] = log 7
 x = log 7 / log [ (21/5) ]
 x = 1.356

anonymous · Answer

thanks love.

anonymous · Answer

ur welcome

hero · Answer

I could have posted that as a solution, but I was too busy trying to challenge myself to express 3/5 as a power of seven.

anonymous · Answer

lol :P