# More logarithm problems

mathdummy
$$log_10x-2$$=0 ....... that's log base 10

ln(x+5)=ln(x-1)-ln(x+1)

$$log_4x-log_4(x-1)$$=1/2

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

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.

#1:

$$\log_{10} x - 2 = 0$$

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

$$x = 10^{2} = 100$$

#3:

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

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

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

$$x = 2x - 2$$

$$x = 2 (x > 1)$$

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