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# Can you solve log sub base 2 (x+1) + log sub base 2 (x+7) =3 with steps showing how you get to the answer?

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Can you solve log sub base 2 (x+1) + log sub base 2 (x+7) =3 with steps showing how you get to the answer? I get to the log sub base 2 (x+1)(x+7) = 3 but I don't know where to go from there.

Jul 9, 2015

#1
+17777
+5

log2(x + 1) + log2(x + 7)  =  3

log2[ (x + 1)(x + 7) ]  =  3

Simplifying the left side:

log2[ x2 + 8x + 7 ]  =  3

Write in exponential form:

x+ 8x + 7  =  23

x+ 8x + 7  =  8

x+ 8x - 1  =  0

Now, finish by using the quadratic formula (You will need to reject imaginary answers and any answer that is less than or equal to 0 (because that will create a log of a non-positive number, which is undefined).)

Jul 10, 2015

#1
+17777
+5

log2(x + 1) + log2(x + 7)  =  3

log2[ (x + 1)(x + 7) ]  =  3

Simplifying the left side:

log2[ x2 + 8x + 7 ]  =  3

Write in exponential form:

x+ 8x + 7  =  23

x+ 8x + 7  =  8

x+ 8x - 1  =  0

Now, finish by using the quadratic formula (You will need to reject imaginary answers and any answer that is less than or equal to 0 (because that will create a log of a non-positive number, which is undefined).)

geno3141 Jul 10, 2015