solve: 2^3z+9=8^2z+1

Answer 1

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 = log₈(1+√33)/2

Answer 2

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!

Answer 3

Oops...I messed up....

Answer 4

and now we see why parentheses are important when doing math online.

Answer 5

in the original problem i just raise all the numbers with powers which got me 8z+9=64z+1

Answer 6

thanks!

Answer 7

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

Answer 8

well played, Reiny.
You are the brainliest!