Question

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!

Answer 9

[AI-generated answer — Explain Bot]

To solve the equation 2^(3z + 9) = 8^(2z + 1), we can start by simplifying the bases of the exponents.

Let's rewrite 8 as 2^3 since they have the same base:

2^(3z + 9) = (2^3)^(2z + 1)

Using the property of exponents (a^(m*n) = (a^m)^n):

2^(3z + 9) = 2^(3*(2z + 1))

Now, since the bases are the same, we can drop them, so we have:

3z + 9 = 3 * (2z + 1)

Next, distribute the 3 on the right side of the equation:

3z + 9 = 6z + 3

Moving all the terms with 'z' to one side of the equation and the constant terms to the other side:

3z - 6z = 3 - 9

Simplifying:

-3z = -6

Now, divide both sides of the equation by -3 to solve for 'z':

z = -6 / -3

Finally, simplify:

z = 2

Therefore, the solution to the equation 2^(3z + 9) = 8^(2z + 1) is z = 2.