How do you solve log_2 10 + log_2 x = 6?

1 Answer
Aug 11, 2016

x=32/5

Explanation:

Using the color(blue)"laws of logarithms"

color(orange)"Reminder"

color(red)(|bar(ul(color(white)(a/a)color(black)(logx+logy=log(xy))color(white)(a/a)|)))........ (A)
This applies to logarithms to any base.

color(red)(|bar(ul(color(white)(a/a)color(black)(log_b a=nhArra=b^n)color(white)(a/a)|)))........ (B)

Using (A) log_2 10+log_2 x=log_2(10x)

Using (B) log_2(10x)=6hArr10x=2^6=64

rArr10x=64rArrx=32/5