Question

2log2-3log2=log2x

I need to show work, please show how to do it

Answer 1

x =
`(1)/(4)`

Explanation:

Using the rules of logarithms

• log
`x^(n)` ⇔ n logx

• logx - logy = log(
`(x)/(y)`)

• logx = logy ⇔ x = y

Given

2log2 - 3log2 = log2x

log2² - log2³ = log2x

log4 - log8 = log2x

log
`(4)/(8)` = log2x, hence

2x =
`(1)/(2)`

x =
`(1)/(4)`