SOLUTION: Given that x = 2ᵅ and y = 4ⁿ, show clearly that log₂(x²y) = 3α + 2n

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Question 1209209: Given that x = 2ᵅ and y = 4ⁿ, show clearly that log₂(x²y) = 3α + 2n
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Log Rules
log(M*N) = log(M)+log(N)
log(M^N) = N*log(M)
Let's refer to these as equations (1) and (2)

converts to the log form
I'll refer to this as equation (3)

Also,






Let's call this equation (4)

--------------------------------------------------------------------------

Then we would write the following
Use equation (1)

Use equation (2)

Use equation (3)

Use equation (4)

I don't know where your teacher is getting the 3 in 3a.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Given that x = 2ᵅ and y = 4ⁿ, show clearly that log₂(x²y) = 3α + 2n
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


This statement can not be proved,  since it is    . 

    To make sure that it is wrong, take a = 1, n = 1.

    Then   =  = 4;  y =  = 4;   = 4*4 = 16,

     =  = 4,


    but  3a + 2n = 3*1 + 2*1 = 3 + 2 = 5 --->  .

So,  this statement can not be proved - - - but it can be  ,  instead.



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