Asked by andrea
solve: 2^3z+9=8^2z+1
Answers
Answered by
oobleck
2^3z+9=8^2z+1
rearrange things a bit and you have
8^2z - 2^3z - 8 = 0
but 8 = 2^3, so that's just
8^2z - 8^z - 8 = 0
since 8^2z = (8^z)^2, this is just a quadratic equation, so
8^z = (1±√33)/2
Since 8^z is always positive, we have
8^z = (1+√33)/2
z = log<sub><sub>8</sub></sub>(1+√33)/2
rearrange things a bit and you have
8^2z - 2^3z - 8 = 0
but 8 = 2^3, so that's just
8^2z - 8^z - 8 = 0
since 8^2z = (8^z)^2, this is just a quadratic equation, so
8^z = (1±√33)/2
Since 8^z is always positive, we have
8^z = (1+√33)/2
z = log<sub><sub>8</sub></sub>(1+√33)/2
Answered by
fiddle sticks!
Raise 8 to the power of 2
8z+9=64z+1
Subtract 64z from both sides of the equation which gives us:
8z+9−64z=1
Subtract 64z from 8z which gives us.
−56z+9=1
Move all terms not containing z to the right side of the equation(we subtracted 9):
−56z=−8
Now solve for z!
8z+9=64z+1
Subtract 64z from both sides of the equation which gives us:
8z+9−64z=1
Subtract 64z from 8z which gives us.
−56z+9=1
Move all terms not containing z to the right side of the equation(we subtracted 9):
−56z=−8
Now solve for z!
Answered by
fiddle sticks!
Oops...I messed up....
Answered by
oobleck
and now we see why parentheses are important when doing math online.
Answered by
fiddle sticks!
in the original problem i just raise all the numbers with powers which got me 8z+9=64z+1
Answered by
andrea
thanks!
Answered by
Reiny
oobleck is correct to point out the importance of brackets
Andrea probably meant:
2^(3z+9)=8^(2z+1)
2^(3z+9)=2^(6z+3)
then
3z + 9 = 6z + 3
6 = 3z
z = 2
fiddlestick's solution is bogus
oobleck is correct the way you typed it
Andrea probably meant:
2^(3z+9)=8^(2z+1)
2^(3z+9)=2^(6z+3)
then
3z + 9 = 6z + 3
6 = 3z
z = 2
fiddlestick's solution is bogus
oobleck is correct the way you typed it
Answered by
oobleck
well played, Reiny.
You are the brainliest!
You are the brainliest!
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