Question

How do you solve `logx-log2=1`?

Answer 1

x = 20

Explanation:

Using the following `color(blue)"laws of logarithms"`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(logx-logy=log(x/y))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) " logx-log2=log(x/2)`

A logarithm expressed as log x , usually indicates that the base is 10.

`"Using (B) " log_(10)(x/2)=1rArrx/2=10^1=10`

Thus `x/2=10rArrx=20`