Algebra solve for z, please help

Question

4^2z/3 = 8^(z+2), I need to show my work, but have been racking my brain and my parents' for hours and cannot figure this out please help.

Answer 1

4^2z/3 = 8^2+z

(2²)^2z/3 = (2³)^2+z

2^4z/3 = 2^6+3z

4z/3 = 6 + 3z

4z = 18 + 9z

-5z = 18

z = -18 / 5

Answer 2

In order to find solve this problem, both base numbers (4 and 8) need to have common base. First thing you need to do is find a common base, which is 2 in this case; 4 is equal to 2² and 8 is equal to 2³. Now, that we have common bases, the new equation can be written as, (2²)^2z/3 = (2³)^(z+2). From here, we can multiply/distribute the exponent from inside the parenthesis by the outside, 2^4z/3 = 2^3z+6. Again, since we have a common base of 2, we can solve for the z value by ignoring the base number and focusing on the exponents. In order to get z by itself, we multiply 3 on both sides to get fraction on the left, therefore, making the equation, 4z = 9z+18. Now, we subtract the 9z over to the other side to get z by itself, -5z = 18. Finally, we divide both sides by -5 to get the result z = -18/5. Hope this helps.