How do you solve log2(x)+log2(x+6)=3?

1 Answer
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Mar 11, 2018

x=−6+√722

Explanation:

When you add two logs with the same base, based on the logarithm rules, it's the same as multiplying them.

log2(x)+log2(x+6)=3

log2(x(x+6))=3

log2(x2+6x)=3

To get rid of the log in order to isolate the variables:

2log2(x2+6x)=23 (2log2 cancels out)

x2+6x=9 (subtract 9 and set equal to zero, so that you are able to factor the equation)

x2+6x−9=0

Since there are no like terms, use the quadratic formula to solve:

x=−b±√b2−4ac2a

ax + bx + c=0

x=−6±√−62−4(1)(−9)2(1)

x=−6±√36−(−36)2

x=−6±√722

x=−6+√722 and x=−6−√722

Remember to check both answers to see if they work, by plugging them back into the original equation (if you do this you see that only x=−6+√722 works)

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