Question 1005734
3^m=81
m=4.  One can take logs, but 3^2=9 and 9^2=81.
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(36p^4)12=24 
36p^4=2
18p^4=1
18p^4-1=0
This can be p^4=(1/18)
p= +/- (1/18)^(1/4).  That is two roots.  You get the other complex ones by setting it up this way:
(sqrt(18)p^2+1)(sqrt(18) p^2-1)=0
the second is p^2=(1/sqrt(18) p=+/ - 1/18^(1/4)
The first is p= i +/- 1/18^(1/4)
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5^n×5^n+4=25 
5^(2n+4)=25=5^2
Therefore, 2n+4=2, since the bases are equal. If we took logs to base 5, the base would disappear.
2n+4=2
n= -1
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4^7x/256=64^2x+2/16^2x−1
4^7x/4^4=4^(7x-4).  That is the left side.
4^3(2x+2)/4^2(2x-1). That is the right side.
4^(7x-4)=4^(6x+6)/4^(4x-2)
log to base 4
7x-4= log 4  4^(6x+6-4x+2)=2x+8
5x=12
x=12/5
This checks.  
The left side will be 50859008.46, which is 4^(84/5)-(20/5) or 4^(64/5)