Question

2log2+(1+1/2x)log3-log(3^1/x +27)=0

Answer 1

2 log 2 + ( 1 + 1/2x) log 3 - log ( 3^(1/x) + 27) = 0

log 2^2 + log [ 3^( 1 + 1/2x)] = log [ 3^(1/x) + 27 ]

log 4 + log [ 3^( 1 + 1/2x)] = log [ 3^(1/x) + 27]

log [ 4* 3^( 1 + 1/2x)] = log [ 3^(1/x) + 27 ]

4* 3^1 * 3 ^( 1/2x)   =  3^(1/x) + 27

 12 * [ 3 ^(1/2)]^(1/x) = [ p(3)^2]^)1/x) + 27

12* p(3)^(1/x) = [ p(3) ^(1/x)]^2 + 27

y = p(3)^(1/x)

12 y = y^2 + 27

y^2 - 12 y + 27 = 0

(y -3)*(y - 9) = 0

y = 3   lub  y = 9

czyli

p(3)^(1/x) = 3  lub  p(3)^(1/x) = 9

1/x = 2            lub   1/x = 4

x =  1/2           lub       x = 1/4

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