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Logarithmic equations

(1/4)^x=8^x-1
(1/2^-x=1.6
3^x/2+1=12.2
log3(7x)=log3(2x+0.5)
log5x-log(15.5)=2
logx-log(x/100)=x
5-3^x=-40
9^2y=66
log2x+logx=11
3logx-log6+log2.4=9
2^x/3=80
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1 Answer

(1/4)^x = 8^(x - 1)
 
(2^(-2))^x = (2^3)^(x - 1)
 
2^(-2x) = 2^(3x - 3)
 
-2x = 3x - 3
 
-5x = -3
 
x = 3/5
 
=====
 
log(x) - log(x/100) = x
 
log(x/(x/100)) = x
 
10^x = x/(x/100) = 100 x / x = 10^2
 
x = 2
 
=====
 
log(2x) + log(x) = 11
 
log(2x^2) = 11
 
10^11 = 2x^2
 
x^2 = 5(10^10)
 
x = ± √(5) (10^5)