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Question

Solve log57x412=log5x+2

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Solution

log57x412=log5x+2
log57x4log5x+2=12
log5(7x4x+2)=12 [loga(MN)=logaMlogaN]
log5(7x4x+2)12=12
12[log5(7x4x+2)]=12 [logaMn=nlogaM]
log5(7x4x+2)=1
51=7x4x+2 (exponential form)
Cross multiplying, 7x4=5(x+2)
7x4=5x+107x5x=10+4
2x=14
x=7

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