Logarithmic equations

Question

(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

Answer 1

(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)