Logarithms

Giulie

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Sep 16, 2009
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I need help with this problem:

Solve for X: log[sub:1w8pqyei]4[/sub:1w8pqyei]x-log[sub:1w8pqyei]4[/sub:1w8pqyei](x-1)=1/2
 
Giulie said:
I need help with this problem:

Solve for X: log[sub:qbdb5aqw]4[/sub:qbdb5aqw]x-log[sub:qbdb5aqw]4[/sub:qbdb5aqw](x-1)=1/2

Hint:

loga(m)loga(n)=loga(mn)\displaystyle log_a(m) - log_a(n) = log_a(\frac{m}{n})

Please show us your work, indicatiting exactly where you are stuck - so that we know where to begin to help you.
 
Notice we're in base 4.

Using the change of base, the right side is log(x)log(4)=12,   x=2\displaystyle \frac{log(x)}{log(4)}=\frac{1}{2}, \;\ x=2

Now, all the denominators are the same and we can shed the logs.

log(x)log(x1)=log(xx1)\displaystyle log(x)-log(x-1)=log(\frac{x}{x-1})

xx1=2\displaystyle \frac{x}{x-1}=2

x=2(x1)\displaystyle x=2(x-1)

x=2x2\displaystyle x=2x-2

x=2\displaystyle x=2
 
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