More logarithm problems

[mathdummy]

log_10x-2=0 ....... that's log base 10
(answer: 100)

ln(x+5)=ln(x-1)-ln(x+1)
(answer: no solution. but why?)

log_4x-log_4(x-1)=1/2
(answer: 2)

[futz]

\ln(x+5)=\ln(x-1)-\ln(x+1)=\ln\left(\frac{x-1}{x+1}\right)


So,


x+5=\frac{x-1}{x+1}


Solve this for x, and you will see that both possible values generate a negative argument in the second logarithm, so there is no valid solution.

[PrudensOptimus]

#1:


\log_{10} x - 2 = 0


10^{\log_{10}x} = 10^{2}


x = 10^{2} = 100

#3:


\log_{4}x - \log_{4}(x-1) = 0.5

\log_{4}\frac{x}{(x-1)} = 0.5

\frac{x}{(x-1)} = 2

x = 2x - 2

x = 2 (x > 1)