Question

I need to know the steps to solve this. I knwo the answer already though.
log base4 x - log base 4 (x-1) = .5

Answer 1

Recall \[\log_a(Q) - \log_a(S)=\log_a\left(\dfrac{Q}{S}\right)\]Therefore, we have\[\log_4\left(\dfrac{x}{x-1}\right)=0.5\]\[\dfrac{x}{x-1}=4^0.5\]\[\dfrac{x}{x-1}=\sqrt 4\]\[\dfrac{x}{x-1}=2\]\[x=2(x-1)\]\[x=2x-2\]\[x=2\]

Answer 2

My apologies:\[4^0.5 \text{ should be rendered as }4^{0.5}\]A careless error on my part. :P