At the x intercept, the graph crosses the x-axis, so y=0 at that point. So just solve for x, when y is 0:
0 = logbase2(x-2)+4
logbase2(x-2) = -4
In plain english, this equation says that the exponent you have to raise 2 to, to get x-2, is -4. Or in other words, 2 raised to the power of -4 is x-2.
Mathematically, you raise both sides to the power of 2, so on the left, the log base 2 gets kind of "cancelled out". So you get:
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Verified answer
At x-intercept, y = 0 so log(x-2)= -4 or (x-2)=2^(-4) = 1/16
So x = 2+(1/16)
x-intercept = (33/16, 0)
To find a x-intercept, just find where the function crosses the x-axis...in other words, set y=0, then solve for x.
y = log2(x-2) +4
0 = log2(x-2) +4
-4 = log2(x-2) (subtract 4 from both sides)
2^-4 = 2^(log2(x-2)) (from definition of a log)
2^-4 = (x-2) (from definition of a log)
1/16 = x-2
1/16 + 2 = x
x = 2.0625
x-intercept = (2.0625, 0), or in fractions
x-intercept = (2 1/16, 0)
At the x intercept, the graph crosses the x-axis, so y=0 at that point. So just solve for x, when y is 0:
0 = logbase2(x-2)+4
logbase2(x-2) = -4
In plain english, this equation says that the exponent you have to raise 2 to, to get x-2, is -4. Or in other words, 2 raised to the power of -4 is x-2.
Mathematically, you raise both sides to the power of 2, so on the left, the log base 2 gets kind of "cancelled out". So you get:
(x-2)=2^(-4)
x-2 = 1/(2^4)
x-2 = 1/16
x = 2 +1/16 = 33/16
y= log2(x-2) +4
at x intercept y= 0
so log2(x-2) + 4 = 0
or log2(x-2) = -4
or x-2 = 2^-4
or x= 2^-4 + 2
=1/16+ 2
so x= 33/16 answer
PROOF---------
Y = log2( 33/16 - 2) + 4
= log2(1/16) +4
= log2( 2^-4) +4
= -4 log2(2) +4
= - 4 + 4 =0