Question

Solve for y:

`2^3 (5^0 + 3^(2y)) = 8 8/27`

Answer 1

We are solving:

`2^3 (5^0 + 3^(2y)) = 8 8/27`

Step 1: Simplify constants

• 2³ = 8
• 5⁰ = 1
• Mixed fraction:

`8 8/27 = (8 * 27 + 8)/27`

= `(216 + 8)/27`

= `224/27`

So the equation becomes:

`8(1 + 3^(2y)) = 224/27`

Step 2: Divide both sides by 8

`1 + 3^(2y) = 224/(27*8)`

= `224/216`

= `28/27`

Step 3: Isolate exponential term

`3^(2y) = 28/27 - 1 = 1/27`

Step 4: Solve for y

`3^(2y) = 3^-3`

⇒ `2y = -3`

⇒ `y = -3/2`