Logarithms

[Giulie]

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

 

[Deleted member 4993]

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:

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

Please show us your work, indicatiting exactly where you are stuck - so that we know where to begin to help you.

 

[galactus]

Notice we're in base 4.

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

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

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

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

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

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

\(\displaystyle x=2\)