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Question

Solve the equation in each of the following.
(i) log4(x+4)+log48=2
(ii) log6(x+4)log6(x1)=1
(iii) log2x+log4x+log8x=116
(iv) log4(8log2x)=2
(v) log105+log10(5x+1)=log10(x+5)+1
(vi) 4log2xlog25=log2125
(vii) log325+log3x=3log35
(viii) log3(5x2)12=log3(x+4)

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Solution

(i) log4(x+4).8=28(x+4)=42
x+4=2x=2

(ii) log6(x+4)(x1)=1x+4x1=6
x+4=6(x1)x=2

(iii) log2x+log22x+log23x=116
log2x+12log2x+13log2x=116
116log2x=116x=2

(iv) 8log2x=42=16log2x=2x=4

(v) log105(5x+1)=log10(x+5).10
5(5x+1)=10(x+5)x=3

(vi) 4log2x=log253+log25=4log25x=5

(vii) 2log35+log3x=3log35x=5

(viii) log3(5x2x+4)=125x2x+4=3x=7


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