Solve for x in the equation 3^x×27^(1-x)=40?

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Answer 1 · 2018-03-03T14:09:56

#x~~-0.1789# to 4 decimal places

Given: #3^x xx 27^(1-x)=40#

Note that #27 -> 3^3#

#3^x xx3^(3-3x)=40#

#3^(3-3x+x)=40#

#3^(3-2x)=40#

#(3-2x)=ln(40)/ln(3)#

#-2x=ln(40)/(2ln(3))-3#

#-x=ln(40)/(2ln(3))-3/2#

#x=3/2-ln(40)/(2ln(3))#

#x~~-0.1788813....#

#x~~-0.1789# to 4 decimal places

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#color(blue)("Checking Left hand side")#

Using: #x=3/2-ln(40)/(2ln(3))#

#3^x xx 27^(1-x)-> 40# so LHS = RHS = 40