Question

What is log(x − 2)(2x − 3) = logx
2

Answer 1

`(x - 2)` is not the base, right ?

Answer 2

Right

Answer 3

\(\normalsize\color{blue}{ \log (x − 2)(2x − 3) = \log x^2 }\) like this ?

Answer 4

Yah

Answer 5

Okay, so we will expand the first log, can you expand `(x-2)(2x-3)` ?

Answer 6

To (x-2)(2x-3) = 2x^2-7x+6 ?

Answer 7

yes

Answer 8

Mmkay

Answer 9

And now we have \(\normalsize\color{blue}{ \log (2x^2-7x+6) = \log (x^2) }\).

We know however, that when we have \(\normalsize\color{red}{ \log( a )= \log (b) }\) , then we are able to conclude that \(\normalsize\color{red}{ a = b }\).

So in our case, `2x² - 7x+6` is "a", and `x²` is "b" .

Answer 10

\(\normalsize\color{darkgoldenrod}{ \log( 2x^2-7x+6)= \log (x^2) }\) turns into ?

Answer 11

There Are Two Solutions
x = 6
and
x = 1 Right
?