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20 votes
20 votes
Please solve this:


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

User Rubiii
by
3.3k points

1 Answer

19 votes
19 votes

Answer:

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

User Amitchone
by
2.2k points