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

Algebra.Com
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(3816)   (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(52778)   (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.



RELATED QUESTIONS

Given that log^a (x)=3.58 and log^a (y)=4.79, find... (answered by Earlsdon)
Given that log a(x)=3.58 and log a(y)=4.79, find log... (answered by scott8148)
Given that log x = 3.7 and log y = 3, evaluate log (x^2 y^3) (answered by Theo)
Given that log x = 5.5 and log y = 1.7, evaluate log (x^2... (answered by reviewermath)
1)if log(x-y)√4=log√x+log√y show that (x+y)=20xy 2) show that... (answered by solver91311)
If {{{ log((x + y)/5)}}} = {{{ log(sqrt(x))+ log(sqrt(y)) }}} where x and y are greater... (answered by solver91311,lwsshak3)
Given that log subscript a(x)=3.58 and log subscript a(y)=4.79, find log subscript... (answered by Nate)
Given that log lower case (x)=3.58 and log lower case a (y)=4.79, find log lower... (answered by stanbon)
show that determinant {{{abs(matrix(3,5, 1, "",log(x,(y)), "",log(x,(z)),... (answered by Edwin McCravy)