Question

What is the solution of log(2x + 6) 8 = 3?

Answer 1

Is it x=-2?

Answer 2

(2x+6) is the base ?

Answer 3

Yes :)

Answer 4

\[\huge\color{blue}{ \log_{(2x+6)}8=3 }\]

CLOSE ATTENTION !
\[\huge\color{blue}{ \log_{(2x+6)}8=3 }\huge\color{red}{ \times \log_{(2x+6)}(2x+6) } \]
\[\huge\color{blue}{ \log_{(2x+6)}8=}\huge\color{blue}{ \log_{(2x+6)}(2x+6)^3 } \]
\[\huge\color{blue}{ 8=(2x+6)^3 } \]

see what I did and can do it from there ?

Answer 5

I think so! Would it be...

Answer 6

Can you (to make sure) explain to me what I did in red ?

Answer 7

I think so! Would it be...\[2^3 = (2x+6)^3\]

Answer 8

Yep, good step!

Answer 9

I'm honestly not sure.. did you set it up so both sides equal each other?

Answer 10

yes, what I did in red is based on a rule \[\log_xx=1\]

Answer 11

What is the rule called?

Answer 12

I don't remember.