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Question

The number of solution to the equation log10x1+12log10(2x+15)=1 is 


Solution

log10x1+12log10(2x+15)=1
For the log to be defined,
x1>0; 2x+15>0x>1; x>152x>1(1)
Now,
log10x1+12log10(2x+15)=112log10(2x+15)=log1010log10x1log10(2x+15)=2log10(10x1)log10(2x+15)=log10(10x1)+log10(10x1)log10(2x+15)=log10(10x1)22x+15=(10x1)22x+15=100x1(x1)(2x+15)=1002x2+13x115=0(x5)(2x+23)=0x=5,232x=5   (x>1)

Mathematics

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