What is #x# in #4^(2x+5) = 5^(2-x)#?

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1 Answer
Tom
Dec 26, 2015

#4^(2x+5)=5^(2-x)=4^(2x)*4^5=5^2*5^-x#

take natural logarithm both side

#2xln(4)+5ln(4)=2ln(5)-xln(5)#

#ln(4)(2x+5)=ln(5)(2-x)#

#(2x+5)/(2-x)=ln(5)/ln(4)#

#(2x+5)/(2x-4)=-1/2ln(5)/ln(4)#

#(2x-4+9)/(2x-4)=-1/2ln(5)/ln(4)#

#9/(2x-4)=-1/2ln(5)/ln(4)-1#

#(2x-4)/9=1/(-1/2ln(5)/ln(4)-1)#

#(2x-4)/9=-2/(ln(5)/ln(4)+2)#

#x-2=-9/(ln(5)/ln(4)+2)#

#x = -9/(ln(5)/ln(4)+2)+2#

#x = -(18ln(2))/(ln(5)+4ln(2))+2#

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