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Logarithmic equations

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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)