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What are the solutions to ^log6(x^2+8)=1+log6(x)

What are the solutions to ^log6(x^2+8)=1+log6(x)-example-1
User Mozcelikors
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1 Answer

15 votes
15 votes

Answer:

x=2

x=4

Explanation:

the range is x>0

Move the expression to the left side and change it's sign to get

log6(x^2+8)-log6(x)=1

using loga(x)-loga(y) = loga (x/y) to simplify log6(x^2+8/x)=1

convert it to exponential form to get x^2+8/x=6

multiply both sides of the equation by x to get x^2+8=6x

move variable to the left

x^2-6x+8

factor out x from the expression

x (x-2) -4 (x-2) =0

factor out x-2

(x-2) x (x-4) = 0

set both equal to 0 and get x=2 x=4

User Alexandre Gattiker
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