Question 851415: Solve. log7 100 - log7 (y+5) = log7 10
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! log7(100) - log7(y+5) = log7(10)
subtract log7(10) from both sides of the equation and add log(y+5) to both sides of the equation to get:
log7(100) - log7(10) = log7(y+5)
since log(a) - log(b) = log(a/b), your equation becomes:
log7(100/10) = log7(y+5)
simplify to get:
log7(10) = log7(y+5)
this means that 10 = y+5 which means that y = 5.
confirm by replacing y by 5 in the original equation to get:
log7(100) - log7(5+5) = log7(10)
simplify to get:
log7(100) - log7(10) = log7(10)
since log(a) - log(b) = log(a-b), your equation becomes:
log7(100/10) = log7(10)
simplify to get:
log7(10) = log7(10)
this confirms that the solution of y = 5 is good.
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