Please solve this: {2}^(y - 3) * {3}^(2y - 8) = 36 Solve for y. Explain please!! Answer only if you can.​

Question

Please solve this:


`{2}^(y - 3) * {3}^(2y - 8) = 36`
Solve for y.
Explain please!!
Answer only if you can.​

Answer 1

y is 5.

Explanation:

`{ \sf{{2}^(y - 3) * {3}^(2y - 8 ) = 36}} \\ \frac{ {2}^(y) }{ {2}^(3)} * \frac{ {3}^(2y) }{ {3}^(8) } = 36 \\ \\ {2}^(y) . {3}^(2y) = 36 * {2}^(3) * {3}^(8)`

Introduce log base 10:

`log_(10)( {2}^(y) * {3}^(2y) ) = log_(10)(36 * {2}^(3) * {3}^(8) ) \\ log_(10)( {2}^(y) ) + log_(10)( {3}^(2y) ) = 6.28 \\ y log_(10)(2) + 2y log_(10)(3) = 6.28 \\ 0.3y + 0.95y = 6.28 \\ 1.25y = 6.28 \\ y = 5`