A manatee surfaced for air 2 times in 60 seconds. how many seconds went by before the manatee surfaced the first time if it held
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log₉(<em>x</em> - 7) + log₉(<em>x</em> - 7) = 1
2 log₉(<em>x</em> - 7) = 1
log₉(<em>x</em> - 7) = 1/2
Take the base-9 antilogarithm of both sides; in other words, make both sides powers of 9:
can also be written as √9 = 3, and
, so the equation reduces to
<em>x</em> - 7 = 3
Solve for <em>x</em> :
<em>x</em> = 10
There's a special case of the quadratic formula called the Shakespeare Quadratic Formula (2b or -2b) that applies when the linear coefficient is even.
If you're planning on solving a lot of quadratic equations quickly, it's good to know.
Here we have
so